One thing I sometimes do to MAKE my weaker fingers do more work is to pretend. I pretend that my first finger is gone :eek: :(
I use my middle, ring and pinky fingers. I do this on songs that I'm familar with. Sure the song may suffer. The thing to remember, we are still having fun playing, and we are growing in our skill by MAKING the "other" fingers to do things they most likely are not used to doing.
The key to making this work is to play any chords in the same way as if we were using the "normal" fingers. Simply substitute the first finger for the middle and so on.
Try it for a month. I think you'll be surprised how your dexterity on all your fingers will improve.