KirjE- the weather side of it would be well briefed and I'm sure the Mil ATC would forward any sig weather reports. As folk are saying, it depends where the refuelling is taking place - it could be on a Notamed 'towline' or on a straight line 'en-route' ferry type trip. In the first case mostly under Mil ATC, for the second, presumably mostly in an altitude block under whichever control is appropriate. There are enough bodies in most large tankers to cover several R/T channels.