Now that I'm level 30 and can buy a scimitar, I repeated my armor experiment, but this time for weapons. The weapons I tested were Stick, Short Sword, and Scimitar (you can't use a normal attack without a weapon, so I had to start at stick).
I chose Training Bot for my victim, because I wanted a bot that was weak enough that it's defense value wouldn't effect the hits much, but strong enough that it might have at least some armor, in case there is some kind of weapon/armor calculation.
I used the same method of tracking 30 hits (only this time, it's me doing the hitting

) and also tracked how many critical hits I made and how many times I missed with each weapon before reaching 30 hits.
Here are the results (in order of weakest weapon to strongest):
1) Stick (5 attack, 5 devs)
Code:
Total Damage: 14963
Avg Damage: 498.8
Max Damage: 545
Min Damage: 458
Misses: 6
Critical: 6
2) Short Sword (15 attack, 125 devs)
Code:
Total Damage: 15090
Avg Damage: 503
Max Damage: 566
Min Damage: 461
Misses: 4
Critical: 7
3) Scimitar (25 attack, 900 devs)
Code:
Total Damage: 15726
Avg Damage: 524
Max Damage: 576
Min Damage: 478
Misses: 2
Critical: 2
Looking at the results, there is a slight upward trend. It looks like if I were to get enough samples I might find that the buf value for your weapon is added directly to the damage you do with each hit (Which is pretty much what I expected going in. It would be nice if armor worked the same way!). Because individual attacks can vary so much (nearly 100 points by the last set) I'd really have to get at least ten times as many samples to really start to have a large enough data set to know for sure. Contrary to popular belief, I really don't have that much time
As for misses and critical hits: Though misses do seem to go down the sample size isn't large enough to draw any sort of conclusion.
In summary: the weapons do seem to help, at least a little bit.