BRS-Florida operates non-stop with the TUI Boeing 787-8 series. Occasionally a 9 series has stood in but I don't know how that affects en-route fuel take-up. Weather conditions sometimes see the aircraft on the outbound sector having to take on fuel on BRS-Cancun, usually at MAN as cavokblues has stated. Both routes are shown as 2 x weekly in summer 2022.
I doubt that BOH would pick up many passengers from most of the BRS catchment if there were no TUI summer transatlantic charters from BRS. If there was no BRS service there would probably be one from CWL instead which is closer to most of the BRS catchment than BOH, and BHX is another option particularly for those in the northern part of the BRS catchment. Thomson and others used to operate summer transatlantic charters from CWL which were well supported and many people find it surprising that no-one does currently.
Slightly perverse, at least superficially considering the summer situation, is that both BOH and CWL usually have more winter transatlantic charters than BRS.