No, being underweight is dangerous too. If you have a BMI under 19 then you are classified as being underweight. This is itself it not dangerous as long as you are eating healthily and around 2000 calories a day. However, a BMI or 17.5 of under is usually classified as anorexia and it is extremely unlikely that you naturally have a BMI that is 17, although it is possible in a few rare cases.
If you are not consuming enough calories and not eating the right balance of foods (fats/carbs/proteins etc) then you're body is not able to function properly, regardless of what weight you are.
Seriously underwieght people often have trouble with fertility and can suffer from heart problems and low blood pressure...the list goes on....
However, I want to emphasise that this is usually caused by lack of nutrition/poor diet. The only reason I am going on about diet is because you said "I only eat relatively healthy things" I may well be wrong but this can often mean not eating enough fats and carbs, or even protein.
If you think that the way you are eating now is similar to what I have described above then you're probably one of those people who is just naturally thin, if not, then think about adding more wholemeal bread, pasta and rice into your diet, as well as some more protein such as fish and chicken, plus fats.