Is it ok to let bread rise in a plastic bowl? I got rid of my glass and metal bowls because they were too heavy for me to lift.
It's not just OK, it's preferable.
If you walk into the back in a commercial small bakery, you'll see that pretty much all of their doughs rise in plastic rising buckets. The first advantage of this is that such buckets have snap-on lids that eliminate the need to waste a lot of plastic wrap sealing in the dough. The second advantage for bakeries (but probably not for you) is that they can be stacked.
The third advantage I can only give you from experience (I can't find a reference): the dough rises faster. I believe this is because unlike metal, ceramic, or glass, the bowl does not conduct away the heat of the fermenting yeast. Presumably a dough basket (another option for you in the "easy to lift" department) would work just as well.
It really shouldn't be a problem. A thick-walled bowl is usually preferred to help maintain an even rising temperature. As long as it is food-safe, you keep it in a draft-free area, and it remains at a consistent temperature, you should be fine.