$200 NLHE Full Ring: Top and Bottom pair on a dry board

Last night I was playing 200nl on Bovada and ran into a spot where I thought I had a pretty good read on a guy. I want to check my thought process on this hand more than the actual hand. BTW this is the 5th hand since I've been at the table so I don't have a read on anyone.

UTG 2 limps in he has 100BB

folds around to me in the highjack with A3 of clubs with 100BB I also limp

folds to the button who has 110BB he raises it to $7 or 3.5BB

the blinds fold UTG 2 calls and I call getting 3.5:1

FLOP: Ah 10s 3d POT: $24

UTG 2 leads for $12

I call, Button calls

TURN: 4s POT: $60

UTG 2 checks

I lead for $28 (not sure why I lead thinking back on it)

Button re-raises $79, UTG 2 folds POT: $167 I have $153 behind

Thought process: I put him on a range of something like AQss, AKss, 10's plus. I don't think he is ever raising pre with A10 AJ or any small pairs and giving the way it played out he obviously wouldn't play KK QQ JJ like that.
So I shove.
Is my thought process good or did I leave any possibilities out? Did I make any mistakes besides maybe not leading on the turn?

Thanks in advance for your thoughts.

Why would the button never raise with AT, AJ or small pairs? I think Ax would be a large part of his range pre as he may be raising to isolate the limpers, the only reason you could take them from his range is the fact that you have an Ace and there is one on the board, leaving only 2 for him to have.

Why did you limp pre instead of raising? Now you have to play a pot OOP without the betting lead which gives us lots of tough spots post flop.

Raise or fold preflop. Personally I don't open weak aces from MP 6-max because a lot of people call with any sooted ace, any decent ace, and definitely any big ace. We're going to be OOP a decent amount of time, have reverse implied odds, and people just don't fold enough in general to make barreling profitable. We also don't flop/turn a wheel/gutshot wheel/FD often either.

As played, you are either jamming or folding. You will face an all-in on almost any river, so the important part here is OTT. The lead is good; you get 3 streets of value from any Ax. People will call you down with AJ/AQ/A10/maybe worse and especially AK. Although we block AA/33, I really don't think we're in a good spot here. I expect to see A10, A4s, 1010, and 33 almost everytime here. This is pretty much never a bluff, especially when it's multi-way and he raises OTT when there's an A out there. I'd probably just fold here. You are only beating spazzed out AK/AQ/AJ, but I think those would more likely spaz OTF than OTT. Most people do understand SDV/relative hand strength to some degree, and don't raise OTF with those hands especially given the dry texture.

Dont limp ever

Reraise flop and bet turn

thanks for the replies. I am mainly a tournament player and im just starting to get into cash games so my views and thought process is a little different than a cash reg probably. BTW he had A10.
thanks again guys.

Raise pre. As for your thought process, he's definitely squeezing there with your listed hands and a lot more. Hard to get more in depth than that unless I understand more about the range you've assigned. You have him mostly on AK/AQ I presume and you believe those hands to raise turn and then call your 3bet?