Depends on the weight of the bird.
1) Half a mile is about 800m.
2) 14000 lbs = about 6 tones, same like couple 4WD
3) Fuel consumption is about 20L per 100km or 0.2l each 1km or 0.16L within 800m
4) density of fuel is about 70% of density of water so .... weight of 1.6L of fuel burned would be about 1.6*0.7=1.1 kg
So if birds mass would be below 1 kg - the bridge will not collapse. But if it would be a pelican with the mass of 9kg - it would be a drama :)