Weight limit would require to much math, not one of my strong attributes but would be interesting to know. The 6x6's are 16', planning on 3' on each end to rest on ground, so that will leave 9' open air to hold a 6000 lb-ish tractor.
The Vermont Dept. of Forest, Parks, and Recreation has been pushing portable skidder bridges for loggers for some time now. They are very similar to what Oldpath05 has built. They have published some designs here:
Temporary Wooden Skidder Bridges. Their "standard" design is 20 feet long and built in 3 sections from 6"x8" #1 Grade Eastern Hemlock. It is designed for up to a 14' clear span. The max load rating is for a 32,000# skidder under full load, or a 50,000# forwarder fully loaded. (It should be noted that in addition to the 6 through-bolts, these bridges also connect adjacent beams using 10" flat head log cabin screws midway between each through-bolt. This helps further stiffen the bridge and assure that loads get distributed among adjacent beams.)
I'm no Civil Engineer, but it certainly seems that as long as the wood is sound, OP should have no problem with his +/- 6000# tractor.
Each 3' end will sit on tar paper, that will sit on ground.
When the portable skidder bridges I mentioned above are used, they generally drop them right on the ground. Generally, getting wet isn't what makes wood rot, it's failing to get dry again. Since they are pulling the bridges at the end of the job, they usually have plenty of time to dry back out again. Also, since they are regularly moved, they have easy opportunities to inspect the panels for excessive rot or other damage.
With the light loads and short span OP has described, he should be OK for years. However, It might be worth considering putting some sacrificial wooden footers under each end and making a dirt ramp up to the bridge. If the footers start to go, you can always replace them. If you use something
highly rot resistant for the footers, you can get even longer life (Black Locust will far outlast Hemlock in terms of rot resistance. A concrete "jersey barrier" or cast block can also make a great footer.)
I made a little footbridge over a small stream years ago by just free-hand chainsawing 3 hemlock logs into beams and lag bolting them together. I put each end on a short length of 6"x6" Hemlock beam, which was in a wet, muddy area. I had to replace the Hemlock footer after about 8 years. The bridge itself was still fine 15 years later when I pulled it out to replace it with something less beefy, but with better footing (my neighbor's almost completely blind dog had trouble with my log bridge, so they made a nicer plank one so she could still handle their walks).
EDIT - added PDFs of the "Standard Duty" temporary skidder bridge designs. If anyone wants the heavy duty design (uses 6'x10' hemlock beams) let me know.