'That's very sweet of you' implies that you're being genuinely sweet towards someone, and they're expressing gratitude. The use of 'possibly' implies uncertainty - perhaps they are unsure what your motivation or true feelings are. It 'could' be very sweet of you. :)

I am hard pressed to find a situation in real life where you would naturally say "that is *possibly* very sweet of you." It negates the entire purpose of saying the sentence, which is to thank someone for being nice to you. If you say "that's possibly very sweet of you," you're actually saying "I'm not sure... it could be that you're being sweet to me, or it could that you're really not being sweet to me." Unless, of course, you're being sarcastic and saying the opposite of what you mean.