Each character has one super weapon that can be obtained by fully upgrading one of his/her stock weapons.
Each player has seven stock weapons but the final result after maximum upgrades yields the same super weapon.
Upgrading is done through the shop at save points. There are two parts to upgrading:
(1) Spamming items which give a low amount of EXP to increase multipliers, and (2) Using items which give a lot of EXP, and that now give even more EXP due to your multiplier, to upgrade your weapon substantially.
An efficient way to build the multiplier is to go to the Creature Comforts store and buy Vibrant Ooze. Apply 36 of those to your weapon and you will have a 3x multiplier. Then you can apply Perfect Conductor for 2577 EXP.