Does consuming a lot of caffeine make my bladder "weaker" in a sense?

Yes and no: Caffeine acts as a diuretic, increasing the production of urine, so you have to urinate more frequently and may have an overfilled bladder. Generally that does not weaken the bladder. But if there is an underlying problem emptying the bladder (like an enlarged prostate), overfilling the bladder can ultimately weaken the muscle activity. Caffeine, like most anything else, is best in moderation.

Bladder irritant: Caffeine has a diuretic effect, so it may make you go to urinate more often, but also it has an irritating effect on the bladder as well. If by weaker you mean you go more often and hold less then yes.