This is one area that I often wonder about. I don't know about New York weather issues, but take for example the 'lots of snow at LHR' one.

For instance, hypothetically speaking, if ramp personnel (e.g. tug drivers) refuse to work while the apron is icy, and based on OHS regulations they can rightly refuse to do so, and as a consequence BA, due to its frequency of services, gets affected more severely than other carriers, should BA be held responsible for that? Or should the situation be deemed to be 'outside of its control'?

We have had a lot of snow here (an European outport), and the conditions on the apron is often atrocious. Far worse than what I have ever seen at LHR. But as far as I know, BA have not had to cancel flights due to weather here, because things still keep chugging along, albeit a little awkwardly. Same with other airlines - we rarely get weather-related cancellations here, despite not having any better facilities than they do at LHR. Snow clearance on the apron is non-existent. So, it is theoretically possible to carry on, and they do 'get on with it' here. Sure, some passengers have gone on their bum by slipping on the apron, but that's the way things are here. Pavements are covered in ice and snow, just like much of the apron. But I would think that if this airport were LHR, the operations would have ground to a halt, not because of BA's choosing but because of the way things are at LHR.

So, what I am saying is, could we actually say that BA has sufficient control over how the weather is handled at a particular airport so that they can maintain operational integrity?

P.S. However, this issue is not something I consider applicable to the OP's situation. He had a confirmed ticket and got bumped. Regardless of the circumstance that indirectly led to his being bumped off, I believe he should be compensated according to applicable regulations etc.