Tons of stuff can cause this. The tire issues shows up most at around 60. BFG's seem to be the worst offenders. Out of round, force variations and of course balance all can contribute. Top it off and there is no isolator between the steering wheel and the tire.
Find a Hunter GSP9700
http://128.242.141.111/pub/search/findgsp9700.cfm
It can check tire uniformity, tire and rim runout, wheel to balancer mounting errors (human), improper bead seating, etc and yes of course, it balances.
For more fun, fleet vehicle often don't use wheel weights. There is a powder that goes inside the tire to balance. No more wheel weights. As the people with the Hunter about it.
Rick