To get rid of the No AP and power up the weapons you need to get the weapon's Crest and Sigil. So you get the weapon and it's Crest and Sigil then go to where you powered up the Cloudy Mirror and talk to the plant thing twice.

Location of each Celestial Weapon and its Crest and Sigil:

Tidus' Caladbolg

Weapon location: Northwest corner of the Calm Lands, behind a mandala at the
bottom of a very narrow hidden trail. Win all four chocobo races, and the
person blocking the pathway will be gone. You _must_ have the Celestial Mirror
in your inventory to get the weapon, otherwise the guard will not move.
(There's no point in going down the trail without the mirror anyway.) If you
won all of the races pre-mirror, and come back after obtaining it, simply win
all of the races again and immediately go to the path the guard was blocking.

Sun Crest location: Yevon Dome, in a treasure chest in the same area where you
fought Yunalesca. You may have to go up and down the stairs once or twice to
get the chest to appear. It's on the left side of the screen, and blends in
with the wall.

Sun Sigil location: After you can control the airship, it's a prize for
winning the fourth chocobo race against the other chocobo rider with a time of
better than 0:0:0. I have no advice on how to do this, other than use the other
rider as a shield if possible, use the D-pad and not the analogue control
stick, and grab balloons like mad. You need between 12 - 15 for a time of
0:0:0. In the Japanese FFX, there was a cheat that made the birds pass right
through you, and therefore this process very simple, but it seems to have been
taken out of the North American - and presumably PAL - release. So the moral of
this story is, practice practice practice, learn Japanese and import the game
so that you can cheat, or check out Morelock's Sidequests FAQ for an in-depth
strategy of how to win this race.

Yuna's Nirvana

Weapon Location: In a chest at the Monster Arena to the east of the Calm
Lands, after collecting at least one of each monster from the Calm Lands.
Although you can find the chest before leaving the Calm Lands, you MUST have
the Celestial Mirror in your inventory to open it and therefore get the
weapon.

Moon Crest location: Besaid Island beach, in a chest in a cove on the east
side, only accessable by swimming. You can get this very early in the game.

Moon Sigil location: Defeat all of your Aeons at Remiem Temple, then preform
the Farplane Sendoff for Belgemine. All of your Aeons means ALL of them,
including the secret ones like Youjimbo, Anima, and the Magus Sisters.

Wakka's World Champion

Weapon Location: After you can control the airship, the bartender in Luca
Cafe will give this to you if you've won at least 5 Blitzball games. You MUST
have the Celestial Mirror in your inventory to get the weapon.

Jupiter Crest location: Luca Stadium, in a locker in the Besaid Aurochs locker
room. You can get this after you've finished everything you need to do in Luca
for story purposes.

Jupiter Sigil location: After winning all four of Wakka's Overdrives, this is
a random grand prize in the Blitzball League game.

Lulu's Onion Knight

Weapon Location: In a sealed chest in the pool at Baaj Temple, hidden in a
corner on the opposite side of the pool from the doorway to Anima's shrine.
The chest will not appear until you've defeated Geosgaeno, and isn't visible
until you're literally right on top of it, so dive deep and keep hitting the
[X] button to search for the chest. You MUST have the Celestial Mirror in your
inventory to open the chest, and therefore get the weapon.

Venus Crest location: In a treasure chest that appears during your second
visit to the Farplane. You can get this after you've finished everything you
need to do in Guadosalam for story purposes.

Venus Sigil location: Dodge the lightning at Thunder Plains 200 consecutive
times by pressing [X], then go back to Rin's travel agency and examine the
treasure chest out front. Do not save in between dodges, leave the screen, or
even blink, because this will reset the dodge counter. (Just kidding about
that last one.) Also, don't just sit there and hammer [X], or use a turbo
controller, because the game senses you're trying to cheat, and will zap you
with lightning just to annoy you. You can get the Sigil on your first visit to
Thunder Plains, long before obtaining the airship, unlike everyone else's
Sigils.

Kimahri's Spirit Lance

Weapon Location: At Thunder Plains, pray by pressing [square] at any 3 glowing
Qactuar stones, then return to the south part of the plain and follow the
Qactuar ghost to a wrecked tower. It's on the right side of the screen,
embedded in the rock wall, equidistant from the north and south boundries of
the plain. Pray there. Although you can find the chest during your first visit
to Thunder Plains, you cannot open it until you have the Celestial Mirror.

Saturn Crest location: Mt. Gagazet, in a treasure chest between the pillars
on the left, just past where you fought Seymour.

Saturn Sigil location: Macalania Woods butterfly-catching game, after
getting the airship. There are technically 3 different versions of this
minigame, each at a different difficulty with different prizes: (1) upon
first entering Macalania Woods, (2) after fighting the Spherimorph, and (3)
after you can control the airship. To start the minigame, talk to the harp-
playing demihuman near the entrance, then touch the blue butterfly. The
object of the game is to touch all the blue butterflies in one area before
time runs out. If you touch a red butterfly, you'll automatically have to
fight a battle, and lose a few seconds. You can find a scan of the suggested
route from the Ultimania guide at
http://home.san.rr.com/circe/ultimania_butterfly.html.

Auron's Masamune

Weapon Location: Behind a mandala at Mushroom Rock Road. At the bottom of the
Calm Lands valley, at the opposite end of the crevasse from the Cave of the
Stolen Fayth, take the Rusty Sword (key item) from the rocky alcove. Then go
to Mushroom Rock Road and continue straight ahead north until you see a little
green square on the area map. (Recall that earlier in the game, during
Operation Mi'ihen, you were diverted to a west exit instead of allowed to
venture north.) It's the second left on the first screen of Mushroom Rock Road.
The green square represents a floating mushroom stone, ride it up to a plateau,
and stick the sword in the ground next to the statue of a warrior standing over
a slain behemoth. The mandala will appear on the wall behind you. You MUST have
the Celestial Mirror in your inventory to get the weapon.

Mars Crest location: In a chest in the old part of Mi'ihen Highroad. To get
there, go north on Mi'ihen Highroad until you reach the entrance of Mushroom
Rock Road, then hang a U-turn and go south.

Mars Sigil location: Unlock any combination of 10 Area Creations or Species
Creations bosses at the Monster Arena to the east of the Calm Lands, and the
trainer will give this to you. Area Creations are unlocked by capturing at
least one of each monster in a particular area, and Species Creations are
unlocked by capturing several of each monster from a particular species -
Bombs, Wolves, or Floating Eyeballs, for example. If this isn't descriptive
enough, see my Monster Arena FAQ for the exact conditions to unlock bosses.

And if the trainer doesn't give the Mars Sigil to you, either a) keep
chatting with him until he does, or b) you didn't unlock enough special bosses
- Original Creations do NOT count towards your total.

Rikku's God Hand

Weapon Location: In a sealed chest at the bottom of Mushroom Rock Road,
accessable by selecting Password on the airship, then inputting "GODHAND".
You MUST have the Celestial Mirror in your inventory to get the weapon.

Mercury Crest location: In a treasure chest in the fourth area (see below)
of Sanubia Desert, in an alcove to the northwest. If your area map is turned
on, you cannot miss this.

Mercury Sigil location: Sanubia Desert, in a treasure chest in the area
protected by a sandstorm. To get rid of the sandstorm, you need to play a
hide-and-seek minigame with the Cactuars after you can control the airship.
(You can examine the Cactuar glyph during your first visit to Sanubia Desert,
but again, you cannot play the minigame until you have the airship.) First,
let's get our bearings... Sanubia Desert is divided into four screens:

(1) The oasis with the save point.
(2) The winding path with the save point inside a tent.
(3) The huge open area with the ruins to the northwest and the save point next
to the large Al Bhed sign in the middle.
(4) The area right before Home with the sandstorm, Cactuar glyph, antlion
pits, and numerous small Al Bhed signs.

To initiate the minigame, go to the fourth area and examine the Cactuar
glyph. You'll then be asked to find 10 Cactuars in the desert. After finding
each one, you'll recieve a green sphere - if you managed to catch the Cactuar
without it looking at you, the sphere will be named, but if not, it will be
called a "Sphere del Perdedor". (In other words, "Loser Sphere".) The more
named spheres that you collect, the better your prize will be. Regardless of
which type of sphere you recieved, take each one back to the Cactuar glyph in
the fourth area after collecting them. The order of Cactuars is is:

(1) Tomay - found in the first area, the oasis, to the right of the save
point.
(2) Rovivea - running around in the northwestern alcove of the second area.
(3) Chava - hiding behind the Al Bhed 20% sign in the fourth area; examine it
to find him.
(4) Alek - running back and forth in the ruins in the northwestern part of
the third area.
(5) Aloja - with Alek.
(6) Vachella - hiding behind the save point inside the tent in the second
area; examine it to find him.
(7) Robeya - hiding in a treasure chest in the southwestern corner of the
third area. This chest contains two Mega Potions otherwise.
(8) Isrra - running around inside an antlion pit in the fourth area. **
(9) Elio - at the oasis, then beams up to your airship and can be found on
the roof.
(10) Flaile - appears automatically after bringing the rest of the green
Cactuar spheres to the glyph.

Once you've found a Cactuar, you don't have to find them again - you can
leave the desert whenever you want, and the minigame will not have reset.

** There is a bug with Isrra where he won't be there. I speculate that if you
find the Cactuars all at once without leaving the desert, you'll encounter
it. Just leave that screen, return, and you can find him. Why on earth Square
fixed the chocobo race and AP trick cheats but not this bug, I don't know.