Yes.
All this talk about adding weight may be misleading. The whole purpose of the trailer is to get weight OFF the vehicle axles (and in some cases fit outsized cargo). Adding too much weight to the tongue defeats the purpose and reduces the overall capacity of the vehicle/trailer combo, and increases vehicle workload (fuel economy and engine wear).
Tongue should not lift itself up. I do alot of towing with M416 and M101. IMO, 100 pounds tongue weight is probably too much, I would look for 25-50 pounds, something easily one-hand liftable. I've run as light as maybe 10 pounds and it will work, but I like a little more margin.
No, there is nothing wrong with the tire design, they work fine up to maybe 85 mph, which is about as fast as I've done. I also tried the bike rack thing. Bad plan. In your case the wind drag on the bike was probably enough to unweight the tongue, sounds insufficient but it happens. I no longer do that, made a rack with fork clamps for the top of the trailer.