Raise more pre and betting about 1/2 pot on flop....

As played, you have a Villain who has not shown any aggression up until now and you're OOP. I'd probably flat flop and see what develops on turn. Once you bet out turn and he shoves....this is always a fold against described villain. KK doesn't play well multi-way and don't want to get involved for deep stacks calling down with a big overpair.

When a rec villain at this level raises flop and shoves turn after you lead out, it means he's got it nearly 100% of the time.

that's what happens when you raise to 15 from UTG in a 2/5 game. all sorts of 3x hands are going to be coming along.

Yeah in my 2/5 game a $15 raise gets called WAY wider than a $25-30 raise. The 3x raise in LLSNL is more of a pot sweetner than a raise that will narrow the field. Deeper stacks mean more implied odds so I'm calling 3x's (and sometimes even 5x's) with a much wider preflop range when I have position on a perceived target (fish, aggro, etc) because I know all it takes is one dream flop and they will never put me on hitting a strong flop because there was a "raise" (like a K6 suited flopping top two for example).

Having said that, I still think T3cc is a bit TOO wide for me but I think there are a lot of people who will call almost anything for 3x but will call maybe half that range for 5X. It's funny the impact that that extra 5 or 10 bucks has on people's willingness to "try to catch a flop".

So like others have said, raise more pre, bet more on flop and it becomes much easier to navigate tough spots like overpair OOP 200+bb's deep because you have more range-narrowing information due to larger raise and bet sizes.

I like the turn bet to be honest. That's where you find out if he has an overpair or flush draw. With 66-JJ its most likely he will call, and with a flush draw he'll happily take those odds and peel.

4 players called pre, there is a strong possibility that at least one of those cards will be a 3, especially as it's live poker, you have a very loose image, and the raise is too small. I'm discounting boats as I think they'd try and play it a bit trickier.

Am I right in thinking that his shove on the turn was 850 into a pot of 480?

This is an easy fold. Sounds like you've been playing well, built a great image, and have your villains where you want them (calling with T3 versus your kings, for example). Wait for a better spot.