I'm not sure why weight training would cause incontinence.
Do you do kegel exercises? If not, you should. I have what's called "stress incontinence" (if I cough really hard or sneeze, I'm likely to pee just a little) and workign on my kegels has helped a lot.
Also, you can use smart balls (they're marketed as sex toys, but they're great for building strong kegels) to help strengthen the kegel muscles. I bought mine from Adam and Eve online, but I think you can also get them through Amazon.com if you'd rather not order from a sex shop!