I've never worried about 2.3 y.o. DS's fat intake as he bf's, but I'm pg and I think my supply is dropping fast as he's suddenly eating loads more.
He doesn't like or will only rarely eat:
cheese
cow's milk
yoghurt
egg (other than in eggy bread)
oil on pasta or bread
dressings and dips
hummous
various vegetables
potatoes
fish
avocado
sauces of most types
butter/marg on bread/toast
mashed anything in any form
He is allergic to some nuts and we're waiting for his current eczema flare to improve enough to try him with some others.
What he wants to eat is plain pasta, plain white bread, cream crackers, oatcakes, breadsticks and raisins. 
The only proteins he's really interested in are tuna mayo, roast & casserole meats, porridge with milk, eggy bread, shop-bought fish fingers (not homemade).
Any suggestions?