did i over bet this

I´m normaly playing limit at UB but latly i have started to test no limit 25buy in. Last night i had following hand and i wounder how i should have maid the bets to get out more of it.
Sadly there were some problem with the hand histoie so i´ll try to write it down like this.

Im at the button its what i think a normal ub 25 nl table with 3-5 callers preflop.
I have kQ unsuited and limp since there are 5 people in allready.

Flop comes with 8,K,K nothing suited
BB bets 0,5 everybody calls so there is 4$ in the pot i bet the pot
BB and an other player calls
turn Q (this made the KQ suited in clubs)
check buy both and when it comes to me i bet the pot (about 16$)
both fold
the BB player i dont know so much about but the otherone was quite tight and i figured him for AK (he than showed A,8 so i was wrong)

I wounder now what amount should i have made the bet for to get the most out of this hand? i think this is the first hand i have had that has anoyed me for longer than one day.

$4 dollars is still better than nothing. That was one way of making sure you did take the pot down.

well it was a 16$ pot so i´m glad about that but still think i could have got more out of it or i´m i just greedy now?

you have the nut hand - either small bet the turn or check it, and hope they hit a hand on the river and (ideally) bet into you.

You pretty much have the deck crippled (by the turn) so you want get much play from opps with any bet you make. (Anyone with a King or 88 will definately let you know by the turn.) Now since the queen clubs hit on turn and crippled the deck, you could wait until the river. I think anything other than a large bet is probably ok. Checking: ok, since you arent hurt on a river card. Small bet: ok, maybe someone with AQ, AA, Kx, JJ, might think they have the better hand or flush draws would still pay to see the river. Big Bet: Scares out the flush draw, med pairs, etc. Only opps that might play are 88, Kx, AQ, Qxc(clubs). However, if they had those cards, they probably would re-raise a small bet and probably give you the same amount of play.

Maybe if the flop was AKx and you held KK, you could start immediately firing away and bet.