I'd definitely talk to your doc or a nurse about this and see what they advise. Sounds to me like he's cluster feeding. My little one was breast fed and was fed about 3-4 oz every 4 hours (6, 10, 2). When he cluster-fed (growth spurts require more calories) he would feed every 1-1.5 hours....some nights I don't even remember feeding him, burping him and putting him back to bed. I turned into an automaton!
Your babe's only 6 weeks old so I think you're ok. Babies won't eat if they're not hungry. Don't give water to a 6 week old please! I can't believe they told you that. Not healthy at all. Every baby's different and some babes require more food than others. My son is now 10 months old, 23lbs and 32" long. Healthy, happy and safely plump.