My Ponytail Palm has half of the leaves that are totally brown. I have cut them off but still getting more. Am I overwatering? Should I transplant to a bigger container?
Likely you have given too much water, yes. Compare your plant to the image on the wiki page for Beaucarnea recurvata and if you have a greater proportion of dead leaves than that it is getting too much water. The plant is adapted to very dry conditions (native to dry northern Mexico) and needs to be kept like a cactus or a succulent, watered sparingly. The roots are perhaps the weakest part, since the leaves and trunk are supposed to be tough and hard.
If possible, remove the plant from the pot and stand the root ball on newspaper to wick water out of the soil which should help dry it out.
Look at more images found on an Internet search and you will note the examples appear to be growing in pots too small for them. This is good, as Kevinsky has pointed out in comments.