The MJ-1 has been around since the 1950s, with several developmental versions having since gone into service. The MJ-1C model is known to be in use at Hill AFB and RAF Lakenheath. It has a load capacity of 3000 lbs and is electrically powered.
In a still from an informational video1 shot at Hill AFB, a MJ-1C is used to move a B61-12 across the parking apron.
Later in the video, the MJ-1C facilitates loading the B61-12 into a waiting Lakenheath F-35A (20-5619).
On a USAF video2 shot at RAF Lakenheath, a MJ-1C is shown loading munitions into a F-35A. (20-5619 features again)
The MHU-83 can handle heavier loads up to 7000 lbs and is in use for handling ordnance at Whiteman AFB.
A B61-12 (mock?) is loaded into a B-2A inside a hangar at Whiteman AFB3 using a MHU-83.
The MHU-141 is a nuclear-certified munitions handling trailer, with a split deck and two axles. It can be fitted with transverse rails, along which several munitions-carrying cradles can be fixed. Its prime mover is the Flight Line Tow Tractor (FLTT), although it can also be moved manually using a webbing strap threaded though its towing eye. It has mounting points at its corners for fitting a cover, giving protection to the trailer's load against weather or against observation.
For specifications see MHU-141/M Munitions Trailer
A B61-12 (mock?) on a MH-141 trailer outside a hangar at Whiteman AFB3.