FTM - advice please

Ladies my son wants to drink his milk/juice all the time he is what I call a "drinker". He will almost chug the whole thing and not eat cause his tummy is full of liquid. I think he only does this with me cause when he is at grandmas house or daycare I get told he eats very well. What can I do to help him eat?  He isn't underweight at his last check up I was told he is at the right weight but I need to increase his protein which I have been trying. Any advice? Has anyone gone through this? He will be 2 Dec. 31st.