oi. BA is the IATA designator for British airways, like SQ and
MH etc.
First cabin is F Buisness equivalent is known as J and eco is Y in
the airline industry. 
I dunno why we got upgraded.
How full the flight is depends on the load for each flight to each
destination 
how u know it was unbalanced? did the flight crew ask for anyone to
move infront?