Is there a word for a person who uses the thesaurus too much?

grandiloquent

a lofty, extravagantly colorful, pompous, or bombastic style, manner, or quality especially in language
—Merriam-Webster

A style or way of using language [which] is complicated in order to attract admiration and attention, especially in order to make someone or something seem important
—Cambridge Dictionary

This term is properly supposed to describe the speech itself ("a grandiloquent turn of phrase," "grandiloquent claims"). But I've heard it used to refer to the speaker as well. Cambridge gives one such example:

I do not want to sound grandiloquent about this, but . . .

To be more in line with strictly proper usage, you might say that your friend likes to wax grandiloquent. But since you're not exactly celebrating high-falutin' language in the first place, you might rather just use it to describe him directly.

More general terms to describe someone who puts on airs, though not restricted to how they use language: pompous, pretentious, or ostentatious. That last one, especially, comes to mind when thinking about someone like that.

It sounds like your friend is an aspiring vocabulist:

Copywriting: Theory and Technique (1959)