Weight (strength) training can be beneficial at anytime to maintain or improve overall health. I would recommend that you consult a certified personal trainer to obtain the best recommendations for exercise to suit your specific goals.

Strength training doesn't mean that you will necessarily "bulk up" if the right type & balance of training is done. It's true that (the same volume of) muscle weighs more than fat, however, building & maintaining muscle mass and replacing fat is going to aid you in the long run for optimal weight loss. Muscle requires more energy (calories) than fat to maintain at rest.

Consider using how your clothes fit rather than the number on the scale (your weight) as an assessment of health & fitness. If you are losing weight too quickly (>2 lbs/week), it's possible that you are losing muscle and actually lowering your metabolic rate! This means that you would have to eat less to maintain the weight... making weight loss difficult to maintain in the long run.