Does US electric code permit running an aerial electrical service wire from a 2-story house to a one-storey outbuilding?
Virginia is on the 2014 code according to the NEC adoption map.
NEC 225.18.1 thru 5 provide clearance requirements.
10’ is acceptable for foot traffic only area.
12’ if there is a driveway.
18’ if there will be truck traffic.
65’ is not excessively long for a single span of an aluminum feeder but I would not try copper. The weight causes more sag thus more tension is required to maintain your minimum height.  Aluminum feeder will cost less also.
We don’t know your total load but a messenger wire probably be enough for 65’ with aluminum. If you go to 1/4” aluminum messenger cable (not a single wire) you now have a ground that can be used with your 3 insulated conductors sunlight resistant type or a multi conductor cable.
Edit: I double checked and these references will be helpful.
6awg aluminum can span that distance NEC 225.6 I do much larger runs so I am used to messenger wires.
If you connect below the roof you need to be 3’ away from any window openings 230.9.A.
Above the roof check out 230.4 for those clearances.
And remember make your run at least 6” taller at the lowest sag point because a hot day the cable may sag that much it really can.