Sorry to be a terminology nit but this is not a check-raise. A check raise is where you are in position, villain checks to you, you bet and villain reraises.
I wrote out a detailed explanation to answer this question with approximated ranges but lost it when I went to submit and can't be bothered rewriting it in full.
Essentially, until you have reads about how villain plays his draws vs made value hands with respect to aggression/passivity and bet sizings, you have to decide what the general population is doing here, and the best play vs it.
I agree that this is a jam or fold spot because playing 2 more streets out of position on such a dynamic board profitably will be too difficult (and beyond-hand -EV tilt inducing).  
 
Consider when villain raises here, he has a range composed of x value hands and (1-x) bluff hands.
Against his value hands you have about 25% equity.
Against his "bluff" hands, you have about 60% equity.
Note that the board is so drawy, unless villain has a personal tendency to spaz out vs donk bets, he's probably not reraising with absolutely nothing. His "bluff" hands are likely to be semi-bluffed FDs & SDs which have good equity vs your vulnerable top pair (you have limited redraw potential).
 
His 6BB raise, leaves him with 16BB behind and if jammed on would need 16 / 48 = 33% equity to call a jam over.
He is usually pot committed but some villains do retarded things, so we assign a chance of folding of 10% to account for the occasisional spaz play.
 
Does villain have enough bluffs in his range that we can jam profitably?
EV(jam) = f * P0 + (1-f) * [P1 * e - J ]
f = % folds = 10%
P0 = pot before jam = 4 + 2 + 6 = 12 BB
P1 = pot after jam is called = 2 * 24 = 48 BB
e = equity when called = 0.25 x + (1 - x ) * 0.6 = 0.6 - 0.35 x
J = cost of jam = 24 - 2 - 2 = 20 BB
 
breakeven when, EV(jam) = 0 so we can solve for x to find ratio of value:bluff hands villain needs to profitably jam here
0 = 0.1 * 12 + 0.9 * [ 48 * ( 0.6 - 0.35 x ) - 20 ]
0 = 1.2 + 0.9 * ( 8.8 - 16.8x )
x = 0.603 ~ 60%
 
Therefore if villain has < 60% value hands in his range here, jamming is better than folding.
I think there are enough draws on the board that you are obliged to jam it in but it's not a fist pump jam by any means.
If you had the read that villain plays his draws passively, calling with them OR more aggressively, shoving with them, this would conditionally affect his raise donk NAI range and reweight his value holdings upwards. If you had such a read you could deduce that villain has a value hand here > 60% of the time, and would consequently deduce that you should fold.