I seem to recall that the trails that the RAF conducted pre-war found (rightly or wrongly) that the jump to .50 over .303 was not worth the weight and ROF drop penalty (the .303 Browning Mk2 fired at 1150 RPM x 8 - 9600 RPM or about 150 RPS - while the AN2 .50 cal fired at 750-850 RPM x 4 = 3,400 RPM or about 55 RPS) - and only a jump to 20mm cannon was worth it.
That being said the last batch of the Fulmar MK2 did swap the 8 x Browning .303s for 4 x Browning .50s so perhaps the RN thought differently - it's also worth noting that the Wildcat F4F-4 had 6 x 50 cals at the insistence of the RN - the USN flyers at the time thought that it was unnecessary and only served to make the aircraft heavier - I guess this reflects their foes - the RN had to contend with 2 and 3 engined bombers and 4 engined Condors most of which had armour and self sealing fuel tanks while the Japanese aircraft had no armour or Self sealing tanks!
Weight wise - an AN2 weighs 27 KGs while the Browning .303 MK2 weighs 10.7 KGs
My google fu has failed and I cannot find .50 cal ammo and link weights
British Browning .303 MG: 7.7 x 56R
Complete Round + Link: 1.06 Ounces
Which is 30 grams
I wonder about the destructive power at the other end, the useful life of the .303 was very short whereas the .50 cal Browning was useful right up to 1945. I imagine the Vickers with its 81mm cartridge might run out of life a bit before 1945, but would be a holy terror throughout Britain's darkest years.