yes, the A2 was a WL trailer, but the typical towing vehicle was not a 3t truck.
First of all you must consider the purpose of these trailers and second the average distance these trailer were moved in daily business. Most of all, for this few meters the trailers were pushed by soldiers and if available by tractors. The only documented exception is a truck loaded with fuel drum towing a Notschnelltanker from plane to plane for refuelling them. This truck was called "Behelfstankwagen" (auxiliary fuel truck).
Only in case of a relocation of a unit these trailers were towed by trucks. Usually to the next railway station and the truck returned to get the next trailer. After arrival of the train at the new location, the same procedure again to the new military base.
All in all the Luftwaffe was always short with trucks, especially prevailed stationary units like maintenance, engineering, communication and airfield operation units.