GM - I've just answered this question on the Professional Flight Training forum. If you have, quite sensibly, decided to move it here, you should delete the other thread.
It's a long time since I flew a helicopter but...
In a still air hover, TRT is, in broad terms, equal and opposite to weight. As the disc is tilted to commence a transition into forward flight, the TRT vector is tilted and must be increased so that its vertical component remains equal to weight if level flight is to be maintained.