Line is fine but turn should be bigger to set up a pot sized river jam. On this particular river I would go for a smaller size (no more than 1/2 pot).
I'm struggling to see checking being better than betting on the flop. The only reason I can see is the range advantage that BB has over us (we have no top 2, top set, middle set etc).
However, we will have a value betting range on this board (aq, 33, a3s) so we should also have some bluffs and qjhh seems like a really good candidate. The main reason for this is the poor playability on later streets. Obviously we can continue on a heart and a 10 but we can't profitably call turns with just a gutter. So would check some flush draws (and bet stronger ones) along with some medium strength hands and some of our completely bricked suited connectors (which can be complete give ups or stabs on later streets if he checks again)
Someone above mentioned that he won't X/F this board and that he just has pairs that he is X/C and his complete misses which are "mandatory cbet bluffs". We hit this board fairly well (not many nutted hands but we have alot of suited aces, some suited kx and gutters with our suited broadway hands so in position we aren't folding as much as some people think on an akx flop so for him to auto bet his misses will not show a profit for him.
This is dependant on villains range preflop obviously as if he is a nit that 3b JJ+ ak then we shouldn't be betting this board at all and especially not with qjhh when we block his 2 most likely X/F hands.
However, if villain has a reasonable range he will have some give ups here as well as weaker to medium made hands that will fold to further aggression.
I guess the main thing is here is that if we are checking back this board all of the time then we are getting to the turn with a very weak range as more of our hands are not very strong on this board. IE if we bet this flop with all of our good hands and check all of our medium and weaker hands then villain can always fold flop when we bet if he's not got it and happily bet turn and river with impunity when we check back. He can also just X/R flop and stack us when we bet because we always have a pretty strong hand.
Knowing what we have (BDFD + gutter) is good. Knowing what villain might have is better. Yet better is knowing what villain might put us on. You should even have an idea about what villain thinks we think he has (i.e. what he think he represents to us by checking).
I think going into leveling wars and making broad assumptions about how people at the micros think and how they think you think when you don't have a sample will just end up with you levelling yourself.
That said there are definite player pool reads you can make but I wouldn't go far away from what is solid unless they give you a reason to.
This is a pretty tl;dr post and iv probably missed alot out but I think it's a pretty interesting spot.