Folding Kings (nearly)

I nearly folded KK correctly the other day. I just couldn't bring myself to do it.

Here's how it happened. You tell me if you would have played it differently:

I ($100) limped UTG for $1, UTG+1 (LAG - $90) made it $4 to go, folded round to the BB (absolute rock! - 8% VPIP 3% PFR, $36 behind) who re-raises to $9.

I was sure the BB's range was AA-KK but called anyway for $8 more.

Flop ($27) came 222. BB checked, I bet $8 (maybe he's got AK, dont want to give a free card to the LAG behind me), LAG calls, BB calls (OK, he's got AA).

Turn another rag. BB checks again, I bet $8 (same reasons as before), LAG calls, BB calls.

River Q. BB checks again, I check (happy for free show-down), LAG bets $30, BB calls all-in for $20 ($10 in side pot), I call $30.

Showdown - LAG 1010 (stupid river bet), BB AA, me KK.