Weak or strong, basing is all about using your legs! If you try to rely on your arms or back to pull a stunt up, it's going to crumble once you do anything harder than a prep. Make sure that your arms get locked out and squeezed by your temples in extended stunts (Never bend your arms in an extended stunt....if you need to stabilize or adjust then bend your knees but keep the arms locked out). Make sure that you and your main base are so close that you are touching for extended one leg stunts (NCA and UCA teach different ways to secondary, so I'm not sure which way your team is using, but UCA would be chest to chest, NCA would be right shoulder in between the main base's chest) and are not stepping back away from the stunt as you try and go up. The main base and back spot should have a good chunk of the weight, and you are there to stabilize and help give the flyer a more solid foundation for her to stand on realistically, so even if you are a 90 pound willow as long as you are locked out and right up on your main base using your legs during dips to get up/down then you will be able to do it.
Leg conditioning (squats, lunges, etc.) can help a good deal, as well as arm toning (to help you lock out, squeeze your shoulders up, and have your arms up in stunts for extended periods of time). I've always found that core conditioning helps all aspects of cheer, also (abs, etc) if you've got the time.