I bought the round plastic kind. How much weight will it hold? I have a 3-light (globes). Will it hold it?

The box must be rated for a fixture and affixed to a permanent building member. Rated boxes have instructions and weight limits noted in the installation paperwork.

What kind of box did you buy? There are two basic types of boxes. The type for new work or construction which are nailed to the framing member and "old work" that are simply clamped in some fashion to the drywall.

Where is the fixture to be mounted, on the wall or from the ceiling?

How does the fixture weigh, at least approximately?

Unless you have some really unusual bathroom fixture, like a wagon wheel converted to a light fixture, the old work box will support it.