I would check out some baggy MTB shorts. You get the benefit of Spandex and padding without, well...looking like you're wearing spandex. These will help with and you should notice a big improvement over just regular shorts. You can find companies that make these shorts in the larger sizes. Like Superman said, normal spandex bike shorts with a pair of athletic shorts over them is another option. You might also want to get some Chamois Butter or something similiar to cut down on chafing/irritation. If you don't like any of the cycling shorts ideas, you could look into some kind of athletic apparel that breathes well.

-Moab