I can honestly say I've never been 99 lbs. But I am close, and fit, and I do do resistance training. Yet the only semi-useful thought I have is this: why is starting as a weak woman different than starting as a weak male? We don't have as much testosterone as men, and therefore build muscle more slowly and must lift lighter weights, but other than that I don't see how our training should differ. Especially at the beginning, when we're not striving for any particular sort of perfection.
I would first assure that she's meeting her protein and caloric needs. 1 g protein/lb of lean body weight is a popular number these days. Lots of calories. And the occasional carb to restore glycogen stores. According to practically every trainer on the planet, if one wants to put on muscle, she needs to EAT. In any case, nothing is going to give her more energy to dominate said 'weakness' than fuel for her body.
Something else I might do is try to include some impact training. By "weak" do you mean simply that she has little muscle mass, or that she suffers from malnutrition? It is important to build bone density, especially in someone malnourished or who was possibly on a crash diet before. And impact exercises can help with that, along with a proper diet devoid of grains/carbs/etc.
And then, since this woman was the one to initiate resistance training, I would trust that she wants to dig deep and build muscle. If she has to start with lower level weights with high reps, accept that. Set a rep number--say--8 or 12 or even as high as 20--and have her use low level weights until she can lift them without too much struggle up to that rep level. Then have her step it up to higher level weights. I remember that I started weight training with 5 and 8 pound curls. And now I do 20 pound curls without any problems. If dumbbells are what she and you want to be doing, don't worry about the fact that 10 pounds is heavy for her. If the exercise she's doing is appropriately strenuous, she WILL see results. And she WILL progress up to and beyond ten pounds, so long as she is diligent and eating well.
And if you/she wants to start with body weight exercises, do so, but just simply. Do knee pushups and lunges of all sorts. I would check out Mark Sisson's new e-book, Primal Fitness, here, for recommendations on easy body weight exercises: http://www.marksdailyapple.com/primal-blueprint-fitness/
I also want to note that even when starting with 8 lb weights I began to see a difference in muscle size and tone almost immediately. Note, too, that I'm 105 lbs, 5'2, and certainly muscle-y. The effects are definitely within her reach. Good luck to you both.