QQ set, 140bb effective, flop and turn sizing?

mp caller is 34-12 with 67% fold to cbet relative unknown
button caller is 11-8-1.3 nit who plays up to 200nl but doesn't seem competent
bb is 18-14 but seems a bit fishy and prone to station behaviour
flop and turn sizing?

Full Tilt No-Limit Hold'em, $0.50 BB (7 handed) - Full Tilt Converter Tool from http://flopturnriver.com

MP1 ($32.40)
MP2 ($20.50)
CO ($51.40)
Button ($62.05)
SB ($59.15)
BB ($70.80)
Hero (UTG) ($85.75)

Preflop: Hero is UTG with Q:heart:, Q:diamond:
Hero raises to $1.75, MP1 calls $1.75, 2 folds, Button calls $1.75, 1 fold, BB calls $1.25

Flop: ($7.25) Q:spade:, 10:heart:, K:spade: (4 players)
BB checks, Hero bets $5, 2 folds, BB calls $5

Turn: ($17.25) 6:club: (2 players)
BB checks, Hero bets $????,

15 to set up for river jam? You say he's stationy.

board's soaking, calling ranges are inelastic vs bet sizes, 2/3 villains are likely stations, i'm inclined to go as big as i feel i can get away with on the flop. you'd have a far better intuition of what size that is than i would.

edit: but i guess to respond with only that would be to not answer the question, so i'll say $6

turn i'd still B/F big, like $14. obv planning to jam a lot of rivers, but we also reduce the implieds for his combo draws. i expect villain to never C/R a worse hand given our line/sizing and that he has stationy tendencies

Only natural to go as big as possible when our range is pretty much exclusively the nuts and villains range is no where nears the nuts.

Villain's range is pretty wide Ax Kx Qx Jx fd, bet $12.5.

$6 flop

$15ish turn as played

Shove river

seems so cool to be $20 here or 11 whichever

Stacks seem too deep for 11. I like 20 bucks tho if we bet calling. 14-16 is boring s5andard cooler type shit.

$11 is a bet for what i think his range is weighted to