Properly crossbraced, it should be possible. Still, if you are right and it is indeed some 2000 pounds, it would still be manageable up to about 25 feet by a group of 10-15 men. The weight can't be greater than 100 pounds per person for 25 carriers, or it would never get to the battlefield. So my original upper estimate of 1500-1650 still stands as the heaviest feasible weight, with some 1250-1350 more likely.
Actually, now that you mention it, you're right, it couldn't possibly be more than 100 pounds per person for it to realistically carry it. However, a bridge that size with that weight restriction, i couldnt see it being reinforced enough to support cavalry. I'm honestly really starting to doubt the physics behind it as being possible.
bear with me here, this is just off the cuff, but wikipedia concerning horses in war, back in ancient times a "Light" war horse was anywhere from 800-1000 pounds. However, for it to use an armored rider (im pretty sure it mentioned his cavalry was armored, right), at least a medium horse is required, which weighs in about 1000-1200 pounds. Add in an armored rider, and we're looking at 1300-1700 or so pounds for a SINGLE cavalry man (200-300 or so for the man, and 100-200 for the armor).
Obviously, for a cavalry charge, we're going to have more than one cavalry man on the bridge, and they wont be moving single file. Realisticly, i would bet they're either moving double or triple file, considering the bridge width of 8 feet (beyond that, its going to get very crowded very fast)
So likely scenario, cavalry will be charging in double file. that's anywhere from 2600-3400 pounds on the bridge at any given moment.
To put that in perspective, a 2001 Nissan Altima weighs about 2945 pounds (so sayeth a quick google search)
So per rank of cavalry man, we're looking at the weight of a good-sized sedan or more depending on what file they use.
This is going to utterly crush your average pedestrian walking bridge (which earlier i estimated at about 4-6" in thickness for the walking part).
I cant honestly see a 30 foot long bridge weighing a mere 2000 pounds able to hold so much weight, however, as established, it cannot possibly weigh more than this for carrying purposes.
I just can't see these numbers working themselves out.
Honestly, i think this is just going to have to be one of those issues where we just agree that suspension of disbelief takes over, and we just assume "it works", because the author said so (i'm sure brandon didnt do terribly much research into the mechanics of it, and just wrote it as is because its a believable situation at face-value)