“results indicated that performing progressive resistive exercise or a combination of progressive resistive exercise and aerobic exercise at least three times a week for at least four weeks appears to be safe and may lead to statistically and possibly clinically important increases in body weight and composition. Results also indicate exercise interventions may lead to clinically important improvements in cardiopulmonary fitness. Individual studies included in this review suggest that progressive resistive exercise interventions with or without aerobic exercise also contribute to improvements in strength and psychological status for adults living with HIV/AIDS.” Source: http://www.library.nhs.uk/INFECTIONS/ViewResource.aspx?resID=238543

So it seems that weight training (resistance training) can benefit patients as it builds muscle tissue, and helps to strengthen the body. But professional medical advice should still be sought if possible, as every patient is different.