Reminds me of a bad joke in a book 'The Funny Side of Flying' by Alan Branson where he quotes an airline Ops manual as saying The position of the senior stewardess (it was a long time ago) is immedieatly under the Captain!
On a more serious note: I am not yet flying for an airline, I mainly fly parachutists, but I treat it in much the same way. I am in command of the aircraft, the buck basically stops with me. However, I do not have 5000 parachute jumps behind, unlike the jump master. If the weather is marginal and they ask me if we can go, I will say "I am happy to fly the aeroplane. It is up to you chaps to decide if is safe to jump." Obviously I pass on weather reports from the drop-zone, and do everything I can to insure they have the right information before they go. Although I am responisble for the flight, I am not going to second guess a highly experinced jumper as to suitable conditions for jumping, as long as it is safe and legal to fly. (I should add that as we mainly deal with tandam parachutist there is almost always a very experinced jumper on board.)