When I started giving my girls water in a sippy it was 1 oz ( I started at 5 months though), not to much so they don't have problems holding the sippy cup own their own. Most of it gets on them not in them for the first few weeks anyways. My almost 7 month old has 3 oz in her sippy cups now she drinks about 1 oz, gets 1 oz all over her and the last oz stays in the cup. I give it to her after she is done eating her solids and it has never affect the amount of milk she drinks or solids she eats.
HTH