Hi Trees,
Just as a pointer, there is an article in the Times of August 1st 1936 under the heading - Territorial Units' Training
It reports that the final contingents of the Territorial Army are about to leave for annual training (the following day).
It states that 45,000 troops will be in training and goes on to list the various camps around the country that will be involved, Weymouth is listed as one of them and is the only camp in Dorset.
The units at Weymouth Camp were;
The Dorsetshire Heavy Brigade - R.A and Fortress R.E
144th Gloucestershire and Worcestershire Infantry Brigade
48th Divisional R.A.S.C (Royal Army Service Corps)
and the 143rd Field Ambulance.
Not sure if it'll help, but you never know!
Mick