My son was very underweight for the first 3 years of life, thankfully caught up and was of an average weight until the age of about 8 years and was then overweight for about 3 years.  Since he went into puberty and we had the growth spurt, his weight levelled out and for the last few years his weight has been stable and entirely normal, even though he eats continuously!  He is now 16 years old and reasonably tall and slim - all I ever hoped for when he was little!  I believe the ups and downs through childhood were due to his medication changes not being quite as fine tuned as they could be.