Barret-Limit(Catastrophe)-Once Meteor is summoned go to Corel and talk to the old Lady.
Weapon(Missing Score)-It's on the steps going up to the S. Ray. Barret has to be in Team.

Tifa-Limit(Final Heaven)-play the music from your flashback... after the Meteor is summoned.
Weapon(Premium Heart)-Go to the store in the Wall Market that has that Machine Gun (with the key to Midgar)

Aeris-Limit(Great Gospel)-get the mythril fro the sleeping man and at the weapon seller open the upstairs box. Use the Buggy and ride the ship at Costa Del Sol to get Her Limit before she dies.
Weapon(Princess Guard)-It's at the end of the hall in the Temple of the Ancients marked IV.

Red XIII-Limit(Cosmo Memory)-Open the safe in Nibelheim(combination in Yuffie/Vincent section) fight Lost Number and the Cosmo memory will pop out when you win.
Weapon(Limited Moon)-Have RedXIII in team and go back and talk to Bugenhagen after Meteor.

Cait Sith-Limit(NONE)
Weapon(HP Shout)-In the locker (in the ShinRa HQ) on 64th floor.

Yuffie-Limit(All Creation)- Beat all five Gods in the Pagoda of her Home Town.
Weapon(Conformer)- In the Crashed Plane under the water in the generator room.

Cid-Limit(Highwind)-Inside the Cargo Bay in the Crashed Plane.
Weapon(Venus Gospel)-after the rocket launched talked to the old guy by the store for awhile and he'll give it to you.

Vincent-Limit(Chaos)-Go to Lucrecia's cave in Disc 2.... then on disc 3 come back.
Weapon(Death Penalty)-"      "          "      "      "       "          "         "          ".