KK vs Axx flop

I can't find the hand to post but it's been bugging me all day, so here was the situation. Cash full ring game $2/4, deep stacks.

I get KcKs UTG, raise 4x, UTG+1 (65/15, only about 30 hands on him) calls, 7 folds.
Flop is Axx all diamonds. I bet 2/3 pot, he calls.
Turn is a random small club.
I bet and folded to his rr, just not sure I played it right, but don't know what else I could do.
Subject: Low pair from EP facing UTG raise

Not a specific hand, more of general situation. $1/2 typical full ring game.

Unknown player raises from UTG, I have 5 spades and 5 diamonds or the like in UTG+1.

In a typical game, can I call this and go set hunting?

My debate is which factor is stronger: 1) getting follower callers and getting paid off when I hit my set vs. 2) the risk of a pf rr.

What are your thoughts, I struggle with this type of decision whether I'm UTG+1 or MP vs. an early raiser.

For your second question, about set hunting, it depends a lot on the player and his stack. You're only hitting your set 1 out of every 7.5 times you see a flop. This means your opponent has to have a stack greater than 7.5 times his raise for it to be profitable. Further, he has to be the type of player you know'll stack off to you should this happen. If you think he's only stacking off every other time, then he needs a stack equal to 15x (or thereabouts) his raise, and so on. There are other factors, such as fold equity post flop and him beating your set, but for the most part those are the two basic things you need to consider when deciding whether or not to call with small pockets. Usually, if I'm in early position and I think it's profitable, I'll call, but if I'm in late position I'll stick in a reraise so I can isolate and play post flop with position. Once you have position post flop after raising, your in much better shape and have more fold equity, so you don't need him to stack off every time to be profitable. (Play position right and find the right kind of player, and you can be profitable if he almost never stacks off.)

First hand - I don't really see how you could have played it different. When you're beat, you're beat.