One thing you neglected to mention was your age. This may play a big part in it. My brother was 5'9" and weighed 120 at 17 years old. He went through a growth spurt and at 22 was 6'3" and weighed over 200. Before anything else you may want to look into your problem with eating. Is it a lack of available things you enjoy eating or a more deep seeded problem? Many of the things I eat day in and day out I don't necessarily enjoy, and I do get asked why I eat them if I don't like them. My answer to this is always, it's not about what you enjoy eating but more about whether what you eat benifits you physically or not. An example of this would be carrots. I personally don't like carrots at all but I eat them every day anyway.

I'm sorry if I beat around the bush with the answer to your question but I would address your lack of interest in eating first. It's absolutely essential to your growth and may in fact be why you're having a problem putting on weight in the first place.