I think that in such age you can try to increase your weight and height effectively with many natural ways.
The most helpful among them are:
- eating regurarly more calories than your body burns (you can use special calculators for planning your daily menu)
- eating more protein (it's a main 'builder' for muscles, that's why you need to include more meat, nuts, dailry products etc. in your diet)
- adding more weight lifting into your exercising schedule (it's another important thing for building your muscles, without such exercises your diet will just cause more fat in your body)
- avoding smoking (it's bad habiit for health in general and it's also one of the reasons for being underweighted)

Also if I were you, I would consult with a doc and get tested firstly if I'm really underweighted and need any treatments. Such problem can be also caused with hormonal imbalance, for example symptoms of low testosterone often include it, especially in case of men.