Do I bet or raise the turn with 16 outs?

PokerStars 0.05/0.10 Hold'em (10 handed) converter

Preflop: Hero is SB with [5c], [3c].
4 folds, Hero completes, BB checks.

Flop: (4 SB) [6h], [Jh], [4c] (4 players)
Hero checks, BB bets, MP2 calls, MP3 calls, Hero calls.

Turn: (4 BB) [Kc] (4 players)
Hero checks, BB bets, MP2 calls, MP3 folds, Hero calls.

River: (7 BB) [5s] (3 players)
Hero checks, BB bets, MP2 calls, Hero folds.

Final Pot: 9 BB

I would lead out the flop with an OESD against 3 players. You could check/raise in this situation, since the 3 who put in a bet on the flop will almost certainly call a raise.

The turn you can bet out if you consider your 15 outs clean. You probably have fewer than 15 outs, since a third heart could make a flush, and someone else could backdoor a better club flush. To adjust for these possibilities, multiply your two heart outs (2h and 7h) by 1/2 and your 9 club outs by maybe 3/4. And you still have 4 outs that give you the nuts. So you should play as if you have 12 outs. Since you'll still hit the best hand more than 1/4th of the time, you can lead the turn against three players.