Yup, everything Derf said is right. That 3 was the very obvious nuts there, and if you CRed him on the flop, he's not likely to think you hold the nuts cause every donk and thier brother [no offense] tries to play trips like you did, go for the turn CR. The turn CR is going to announce your hand loud and clear, and your not going to get called by very many hands, and the hands you DO get called with would have put in lots of flop bets, and still bet the turn after you called the 3 bet (AK for ex) allowing you to get your CR off anyway.

Also, if he has a good king he may flat call the raise and then raise your turn bet, enabling you to threebet him on turn, which is the ultimate coup.

Ace high is checking behind and folding the river, whereas ace high might peel the flop.

A middle pair is folding to the turn CR, but may consider calling you down if you bet instead of CRed. But, a middle pair may very ewll just check behind, and possibly fold riv depending what comes down, or may call your bet, thus resulting in 1/2BB more value than raising flop. May or may call riv, depending on what his pair is and what the board is, so 0.5bb more than flop CR.

So basically, mid pair is the only hand your CR is a better play against, caues it makes a teeny bit more. However, when he fires the turn, i am not inclined to put him on a mid pair anymore. Then again, meh.

Point is though, in Shorthanded games especially (where things are more aggro), you oughta play the nuts aggresively because you allow the other guy to overplay his hand more, whereas if you telegraph the nuts with a turn CR, your more likely to get him to slow down, and/or (worst case scenario) make a 'heroic fold'

--

King on turn: Okay, thats a gay card, esp considering hes betting. Most shit is gonna fold to you, though something like a middle pair might not... Kings gonna obv three bet you, and you can probly safely fold there, but if he gets clever and raises your river bet, that almost prices you in to donkoff a bet and have him show you his king. Acehigh is also gonna fold to the turn CR.

So basically, TURN CR:
King standardly played:, fold to a threebet -2BB
King cleverly played, -4BB
Acehigh: +1bb, hes not calling
Mid Pair: may call may not, +2BB

Flat call/donk riv:
King standardly played: -3BB (assuming yuo call river raise)
King cleverly played: no clever play here, -3BB
Acehigh: I think acehigh calls the river here alot, thinking he's priced in and that your either bluffing with air, or chopping +1.5bb
Mid pair, calls here alot +2bb

I have no fucking clue, seems really really close. Flop CR is a no brainer though.