Is eyelid ptosis a weak muscle problem and can that muscle be strengthened with exercise?

This is a good question. Ptosis usually results from the levator muscle loosening or stretching.  Rarely it is from underlying weak muscle.  Neither case is going to improve with any muscle exercising.  The only real treatment is tightening the muscle to make it "stronger".  See an oculoplastic surgeon.

In ptosis, the tendon which is attached to the muscle gets stretched and the lid will droop.  There are no exercises you can do to strenghen the muslce.  The only option is surgical repair.   

Exercising the upper eyelid will not cure or correct your ptosis.  Acquired upper eyelid ptosis is often the cause of an issue with the tendon and not the muscle itself.  Opening and closing the eyelid is actually just as likely to further weaken the upper eyelid.  Surgery shortens the tendon to repair the ptosis.