I have two very little ones, both at one stage classed as FTT.
DS4 is 2 and just over 9kg and DD3 is 3 and 10.5kg (they are short also). There was some concerned at times and for my DS saw peads and had numerous test but all came back fine but now even though they are small their peads are happy because the are happy and healthy.

I am about 47-48kg and 166cm tall so genes do play a part in it.

With the infections a multi vitamin like pentavite may be beneficial also some probiotics which can help to build up the immune system.

The other girls have made wonderful suggestions on the 'fattening up' foods I find graving rather than big meals is better, I think most kids do that though.