Sounds like the nurse wasn't very helpful at all.
As other posters have said if he is healthy, happy and engergetic as you say, there isn't really a problem.
However, dd (2.5) has allergy issues and can't have eggs or dairy. Her weight gain had really dropped off, and the dietician advised that we needed to find ways of getting fat into her diet.
Some of the suggestions she made were:
chicken schnitzel (in breadcrumbs), fried in olive oil.
Lamb chops (dd loves gnawing on lamb cutlets, as they're an ideal size for little hands to pick up)
Plenty of margerine in mashed potatoes - in your case as, dairy is not an issue, you can use butter instead. A little cream added is also yummy.
Also, suitable for your ds, try lots of cheesy sauces with veggies, pasta etc. Have you tried making your ds smoothies? He may prefer this to milk on it's own.
Does he like things like rice pudding or custard? Can be served with fruit so that it's balanced nutritionally.