KK (with re-draw) vs. a possible made straight or flush

[DP388]

20/180 - Villian is a loose donk who has called large raises and cold called re-raises with very vulnerable hands (i.e. KQs) and will chase a draw. Doesn't mean he necessarily has one here, but his flop call was pretty fast. Note: I have Kd

PokerStars No-Limit Hold'em Tourney, Big Blind is t50 (9 handed)

SB (t1595)
Hero (t2585)
UTG (t7505)
UTG+1 (t1825)
MP1 (t1900)
MP2 (t3525)
MP3 (t1305)
CO (t3900)
Button (t3085)

Preflop: Hero is BB with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">5 folds</font>, CO calls t50, <font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises to t250</font>, CO calls t200.

Flop: (t525) 7[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets t300</font>, CO calls t300.

Turn: (t1125) T[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>

Hero: ?

I've already decided my flop bet is too small because I need to be charging a player like this the maximum since he is likely calling, but I was trying to control the pot size.

But I'm really wanting feedback on the turn play in this hand and other situations where possible draws are made.

A check here gets bluffed at often. A small bet will be perceived as weak and a larger bet only gets a worse hand to fold or wastes chips if villian pushes.

It feels like c/f is weak, but it still might be correct. What is the optimal line on the turn and/or river?