Like I said, I think this is close on every street, so I'll lay out some reasoning here.
Flop - I think this is a check back, but its kinda close. Because I have the gutshot, I don't need the c-bet to work as often. However, if I get check/raised, I'm going to be forgoing a lot of turn cards that could help me. But then again, he's pretty passive, so he won't likely check/raise, but he also won't likely fold. I honestly really can't decide, which is better. If he were deeper, I'd like a bet more, so we have a better shot at cramming it all in if we hit a K or a backdoor flush.
Turn - I don't think we can bet the turn for fold equity. I've seen him call the turn with gutshots before, so AT, AK, Jx, and probably 7x are calling. So the question mostly becomes, can I v-bet ace high here on the turn?
Given this simulation (http://www.propokertools.com/simulations/show?b=7s+Qs+Jd+6c&g=he&h1=Ad+Td&h2=*s*s%2C+89%2C+9T%2C+T8%2C+J*%2C+Q*%2C+AK%2C+AT%2C+99%2C+88%2C+78%2C+67%2C+57%2C+T7%2C+47%2C+97), I'd say no. Maybe if I had turned a flush draw, I'd have enough equity to fire, but bleh, I really think trying to bluff this guy multi-street is pretty ugly. I think at 100NL, the fish usually have learned not to call multiple streets with a gutshot or 2nd pair, so this might be better at the stakes you play WV. But in this spot, I really dislike a 2nd barrel, especially since one of the gutterballs he calls with (89) also turned an open ender, and I don't beat two of the gutshots (AT & AK).
River - Given his play before, I expect him to try and slowplay Jx, or any full house. So when he bets, the only hand I expect a passive guy like this to bet for value is Qx. So given his bet size, I need him to be bluffing 32% of the time to be break even.
I ran a simple simulation here (http://www.propokertools.com/simulations/show?b=7s+Qs+Jd+6c+Jc&g=he&h1=Ad+Td&h2=*s*s%2C+89%2C+9T%2C+T8%2C+Q*%2C+AK%2C+AT), and grouped Qx with all the hands he could get to the river with that have air. And even if he has Q2 in his range, I pretty much have enough equity to call. Now his VPIP is probably around 60%, so he doesn't likely have the off-suit Q2/Q3/Q4 type hands in his range. So if I remove Q2-Q7 off suit hands, I get 41% equity. (http://www.propokertools.com/simulations/show?b=7s+Qs+Jd+6c+Jc&g=he&h1=Ad+Td&h2=*s*s%2C+89%2C+9T%2C+T8%2C+AK%2C+AT%2C+Q2s%2C+Q3s%2C+Q4s%2C+Q5s%2C+Q6s%2C+Q7s%2C+Q8%2C+Q9%2C+QT%2C+QK%2C+AQ) So I think the river is probably a call, but that might be results oriented since he showed down 89o. Plus some of his spades will have a pair (like 56s) that he won't turn into a bluff as well, and he'd likely min-raise AK and AQ preflop at least, so we can probably discount those as well.
Course, this assumes that he acts logically and bets his air & queens on the river. I wouldn't be surprised if villain just decided to bet 67 in this spot, because "I haz pair!". So I don't think its a slam dunk to call or anything, and a fold probably has a lot of merit. But I think its fairly close.