Bet sizing question--drawing value from monster hands

SB is VPIP/PFR: 23/13 over 60 hands, and has 50% fold rate on each street (50% fold to cbet); not a very large sample, so I'm just considering him a normal player. First--I haven't played in a while, and I'm thinking I need to reevaluate having played this hand at all, but that isn't really my question.

Given my hand and the flop, how do I size the bet here, as he started at a 49 BB stack, given his stats?

(Note: I'm not expecting much play out of the VPIP/PFR: 8/7 BTN with 65% fold to cbet over 800 hands, and relatively low AFq post flop.)

Really I'm trying to get value out of draws and medium pair, while building the pot. . . I'm just not sure of the sizing.

Merge - $0.04 NL - Holdem - 7 players
Hand converted by PokerTracker 3

CO: $16.13
BTN: $1.14
SB: $1.96
BB: $4.32
UTG: $8.24
Hero (UTG+1): $4.00
MP: $3.71

SB posts SB $0.02, BB posts BB $0.04

Pre Flop: ($0.06) Hero has 5 5

fold, Hero raises to $0.08, fold, fold, BTN calls $0.08, SB calls $0.06, fold

Flop: ($0.28, 3 players) Q 5 J
SB checks, Hero bets ??

I guess in general against a moderate, fairly passive villain, my general question is how do we draw value on boards that might be scary to the hero come turn or river.