Did Quint Respect Brody???
On the boat I think he understood that Brody wasn't a man of the sea and wasn't bothered by it, unlike Hooper who was openly hostile towards Brody at times.
But at the town hall meeting after Alex Kintner was killed, I think Quint actually showed more respect to Brody than he did to anyone else in the room, including the Mayor. Maybe he recognized that Brody was the only person on the island with any sense of how dangerous this shark really was (Hooper made a similar observation). Brody was the only person willing to do the necessary actions, as painful as they may be in the short term, to resolve the problem quickly. And Quint probably realized that Brody would be the person that agreed to give him the money he asked for.