There is only 1 reason why British Airways is opposed to RWY3 and that's because of 1 stakeholder - British Airways.
BA already get somewhat preferential treatment over other airlines; heck they get their own exclusive airport terminal and a high proportion of the slots. Should the additional capacity (eventually) get the go-ahead, it would open it up to all-comers, such as the LCCs.
Every decision is fuelled by their own self interest. The Davies Commission came up with the wrong answer for the government, so it became a whitewash and waste of money!