He may be a "puddle fish". Some Bettas just really do not like to be in larger tanks. I have 2 who get extremely upset about being put into larger tanks, even if it's only .5 gallons more water they just don't like it.
If you want to move him to a larger tank I would try gradually doing it, you say he's currently in a 1.75 gallon, maybe try moving him into a BettaBow 2.5 gallon. PetCo and PetSmart both sell them, however I would replace the filter in there with the Tetra Whisper In-Tank filter, which is good for up to 3 gallons. It's small, and it doesn't have a strong current. Also, your Betta isn't able to get his fins caught and torn up in it, PLUS the filter pads are only like $3 for a pack of 2 at WalMart and the filter itself is about $10 there as well.
If he likes that you can either leave him in there or eventually try the 5 gallon and see how he does in there then.