The bare conductor is about 1.05 lb per foot. Insulated wire weight varies by type of insulation.
0.75 pounds per foot
From the question it is hard to establish whether the service size is 350 amps or the service conductors are 350 MCM in parallel. If the service is 350 amps, the grounding conductor is #3 bare copper wire. Parallel 350 MCM conductors will allow for a 600 amp service. The grounding conductor for a 600 amp service is a #1 bare copper wire.
what is the weight of 300 MCM Copper wire
2.2 lbs per ft
There is no defined AWG for 350 MCM. The American Wire Gauge stops at 0000 (4/0), and 350 MCM is bigger than this. An approximate conversion would be 6/0, if there were such a thing. Extrapolating out from 4/0, 6/0 is 334.8 MCM, and 7/0 is 422.2 MCM. These wire sizes don't exist of course, and don't exactly match 350 MCM anyway.
The diameter of an insulated 750 MCM copper wire is 1.25 inches. The insulated 750 MCM copper wiring has 61 strands and has a weight of 2.7 pounds per foot.
500mcm 37 strand copper wire = 1.544lbs/ft.
A 350 MCM aluminum conductor with an insulation factor of 90 degrees C is rated at 260 amps.
750 MCM (61 strands) 2.316#/ft 750 MCM (7448 strands) 2.719#/ft
1.385 pounds per foot
A 1000 feet of 300 MCM wire weighs 1021 pounds. It is easy to calculate from there.