Why Lifting Weights is Good

1. Improves your cognitive function:  it stimulates your brain.  Several studies have been done that show marked improvements in various mental activities: coordinating multiple activities, focus, and long term planning with both anaerobic and aerobic training. (http://scholar.google.com/scholar?hl=en&q=Exercise%2C+Brain+and+Cognition+Across+the+Lifespan&btnG=Search&as_sdt=0%2C11&as_ylo=&as_vis=1)
2. Increases your metabolism. Stressing the muscles causes them to grow, causing a larger percentage of your body weight to be muscle, which increases your metabolism and thereby decreases fat.  This is in contrast to low intensity exercise or endurance exercise where muscles do not grow much larger, so while calories are burned during aerobic exercise, the number of calories your body burns during normal operation is smaller than in a strength trained individual who has more muscle mass and therefore more resting energy requirements.  (http://scholar.google.com/scholar?hl=en&q=resistance+training+resting+energy+requirements&btnG=Search&as_sdt=0%2C11&as_ylo=&as_vis=0)
3. Increases bone density.  Stressing the bones causes them to grow thicker and denser. Again, while aerobic exercise can help in this area, high intensity exercise helps increase bone density more. (http://scholar.google.com/scholar?q=resistance+training+increases+bone+density&hl=en&btnG=Search&as_sdt=1%2C11&as_sdtp=on)
4. Decreases the risk of injury.  If you are stronger, you're less likely to get injured during competition, or in every day life. (http://www.mendeley.com/research/effect-neuromuscular-training-incidence-knee-injury-female-athletes-prospective-study/ , http://scholar.google.com/scholar?hl=en&q=strength+training+injury+prevention&btnG=Search&as_sdt=0%2C11&as_ylo=&as_vis=0)

All of these things are good for guys and girls.  Actually I think a lot of girls shy away from strength training because of the fear of appearing big.  This is unlikely to happen.  Most guys have to put in a lot of effort in order to gain size working out.  Its way harder for girls, because females lack the testosterone that guys do so their muscles don't develop nearly as much.  If anything any fat you have will be replaced with muscle, and you'll look trimmer even though you are heavier.  Losing weight does not necessarily equal looking thinner.