Using a name as a contraction with "is", syntax looks possessive?

"Bob is fat."

Would it be proper to do "Bob's fat."?

To me, this looks possessive, as if we're talking about his fat rather than using "fat" as an adjective. What's the proper way to do this?

"Bob is fat."

The answer is that it's grammatically proper to write or say "Bob's fat," yes.

It indeed looks (and sounds) the same whether the intention is "Bob is fat" or "The fat of Bob." The difference in understanding would need to come from the context, in writing, or the context or inflection, in speech.

So if the context does not make it clear the precise intention, then it would be smarter to use "Bob is fat" as that phrase is quite clear.