FWIW, I should have been specific to state that at the weight stated, Synergy will almost certainly point you towards one of their PA28s rather than a C152.
I learnt on a C152, and at 15st, it was an interesting conversation with the examiner before the skills test when doing the w&b. That was actually my biggest worry before the test. A mild shrugging of shoulders and the comment "as long as you are aware" was all that happened.
I know exactly where the POHs are for the planes at Synergy, as do l the instructors and students once they've done the first few hours. You are taken through all the paperwork, and specifically how to do w&b checks, and performance based on pressure/density altitude, takeoff and landing distances etc. I am sure that's the same everywhere in the UK, or at least it should be.
What's always concerned me is the insurance aspect, and that in the event of a bad day, one of the first things the AAIB will look at is the w&b.