Which one is correct?
- I hope I thanked you proper!
- I hope I thanked you properly!
I hope I thanked you properly. Properly is an adverb, modifying the verb thanked.
In general, adverbs in English end -ly, and adjectives do not. There are irregular adverbs like well, and others like hard (which does not mean hardly).
Some may say that although properly exists as an adverb, proper may be an adverbial form too. I contend that it is not one in Standard English.
It can be used as an adverb in dialectal English (“Can’t she talk proper?” would not be out of place in south or east London) and it does exist in the fixed phrase good and proper (“I fixed it good and proper; it will never come apart!”) where that entire fixed phrase becomes an adverb.
In Standard English, the adverbial form of proper is properly.
The related question about strange/strangely is worth a read.