I wouldn't have thought that weights would make a huge amount of positive difference for a half marathon, to be honest.
Probably circuit training is more use than weights, but in terms of weights, I do things like the lateral pulldown, bench press, seated rowing to strengthen back and chest muscles. Lowish weights, high reps (eg sometimes on lat pulldown I will do 2 x 30-40 reps at 28kg plus 1 x 20 reps at 35kg, rather than straining away at a high weight for 3x10 reps).
If you are worried about weighing too little, then you'd presumably want to work on the big muscle groups, eg back and chest muscles and also the leg press.
My HM PB is weak, the distance is outside my range, really, but for the record it is 77.31; I am 5 ft 8 and weigh 10 stone.