is water filling up my son? HELP

i am going mental with my son’s eating habit, so firstly we have had issue with him eating solids since its introduction! he won’t eat much but still relies on his bottler. He would drink min of 500ml of formula at night but it’s been a month where we have switched to milk before sleep then if he wakes up at night we would give water and then formula when he wakes up again. Now he is drinking the same amount of water but his eating during the day hasn’t IMPROVED! Now can water fill him up and make him feel full during the day? what do we do? he weights 10.1kg which is on the smaller end for his age !