I have had a good run of cards and have been very active the last orbits.

I have a 1200 stack and pick up [As] and raise to 15.
A 22/15 gut who is decent repops me to 55. He has 550.
I 4-bet to 180 total, he calls.

He has 370 left

Flop [Kc][5s] (366)
Check / Check

Turn
I bet 150, he calls

Should I have bet here?
Should I just give up the hand?
Is there any chance he has QQ, or is it only AK or KK?

Input please

I opened from UTG + 1 and he re-raised from button.
The only real history is that I have been bullying thetable the last two orbist where I have picked up QQ once and AK twice, and some other good hands.

My own thinking in retrospect:

When I 4 bet this big he has to put me on AA, KK, AK, and very rearely on QQ.
His range has to be pretty much the same.

When the flop comes his range is:
1 AA
1 KK
4 AK
4 QQ

If he has QQ and sees this flop, and the range he is putting me on he cannot put more chip in there. There is nothing he beats. And he won't try to bluff with QQ, or with AA.

So I think it is a check/fold for me?
I am just not beating anything.

Now I didn't do that, and got it all in against his flopped quads.

The good side of the story is that I got AA in the BB on a $600 table 30 min later. The very same guy limped UTG, and I raised. He called. I bet a rag flop, and he became all aggro - rasing my flop bet and betting turn. I thought he could have hit a set, but could not lay it down. We got it all in. He had KK. And I won slightly more on that hand than the 550 I lost on the above. He left the table.

What site is this on?

Ongame (Betsson skin)