Adding 48" planks to widen a 36" bridge with no support at ends
Assuming reasonably equal weight distribution, each wheel of a 600 lb. mower and a 200 lb person would carry 200 lbs. Any 2x4 or wider SPF lumber that's reasonably free from large knots will suffice. 

The actual calculations are difficult due to the unknown weight distribution (front/rear, tire width, tire pressure, etc.), but experience tells me that you certainly will not break 2x4 or 2x6 (or larger) lumber in that application, especially if you were to run a sleeper under the ends to tie the boards together and distribute load. I consider that overkill, though, and I'd only bother to do it if you see substantial flex in the individual boards as you roll over them.