Without knowing the wall thickness of the tube.....off the cuff....I'd say the max for that structure is about 2500# presently. Based on the fact that you are spanning a little shy of 20' and deflecting ~1/4" with ~1200# of ATV's.
There is FAR more that goes into engineering calculations.....but for anything but the shortest of spans (where stress/shear become a factor).....L/360 deflection is usually a pretty good rule to follow. That is the length in inches divided by 360.
So say your span is ~18'....thats 216".......and 216/360 is 0.600" deflection MAX. And since you are nearly half that with teh ATV's.....safe to say thats about half the max load that structure will handle.
Then of course you have to have sufficient decking to handle the wheel load of 2.5' crossmember spacing.
Also throw in the fact that the entire weight of the truck or tractor are NOT right in the middle at the same time. A full sized pickup has a lengthy wheelbase. But then you also have to account for dynamic load/stresses of the vehicle moving.
I would forget the aircraft cable and truss it with some rebar similar to whats pictured above but on the BOTTOM so it stays in tension. That will add tremendous strength. But dont just weld the ends at a small point where the rebar comes back to the bridge. Flatten it back out so you get a good 4" or so of weld. Some 3/16 x 2" flat would work too.
Whatever modification you make, slowly work the weight of the load up and keep an eye on deflection. Dont go past 5/8" or so