The math is easily understood. A roof can support a ton with ease. Just look at when a roof is being built, especially a tile roof. A supply truck will load a roof with a conveyer belt and the crew will place the new tile material in a very dispersed way, not placing too much weight on any one roof rafter. Tile or asphalt shingles will easily be several tons. Also, in a snowy environment, a roof is designed to handle the weight of say three feet of snow on it.I do questions that math and the variable supplied by the OP. What that means is that the roof of this building will support my 3/4 ton diesel pickup (scales out empty at 3.5 tons), fully loaded, if I park it on the roof. I just don't buy it.
As for damage being required before a complaint can be made, not so. There are strict codes requiring all water drainage to be carried out to the street. Water drainage cannot run across a neighbor's property, whether its your side or back neighbor. That is code in at least CA. The same building and safety code should be required of shedding snow from a roof. Snow can blow onto the neighbor's property but cannot be naturally dumped from a roof onto his property. The high risk of safety and damage just compounds the complaint.
Snow that slides off a roof can crush the hood or roof of a car. Happens all the time. It slides off a roof with such force it could kill a person which is why you see commercial signs warning people not to stand too close to a snow covered roof. Also, 2,800 pounds is not 2.8 tons. It is 1.4 tons. And, snow could easily knock over a fence if it hit it with the right angle and force...at least the pickets.
True, the OP can wait for damage and then file a claim against the neighbor's homeowner's policy. A few times of doing that and the neighbor will find his own way of fixing the problem. Or, he can file a complaint against the building permit that allowed it in the first place. Just because a building permit was issued doesn't mean the city doesn't have to fix their mistakes.
There Mark, is that sufficient commentary?
Introducing velocity to the equation, as it pertains to the force of snow sliding off of a roof, changes things immensely but mass is still mass and this is a forum for discussing physics.
Your neighbor was granted a permit and, at this point, you can't do a lot about it until something happens...or you can hire an attorney to help remedy the situation. I don't believe that you'd be successful in recovering snow removal costs though you may be able to recover costs from damage due to snow falling off the roof but that would require you to allow something to be subject to that damage.
Alas, winter is coming.
"Where do those stairs go?"
"They go up!"
Does your county have a minimum setback from the property line for structures such as sheds? Even though my county doesn't have zoning there are certain regulations we have to follow, such as a ten foot setback from the property lie for structures like sheds and single family homes.