HI Katy, sorry to hear about your feeding problems. First off, if he's gaining weight well and not excessively then that's the main thing, although I know how exhausting it is when baby is on a 2-3 hour schedule, believe me. But it is actually not very unusual in the first few months and six and a half weeks is still early days. You may hear of a few babies who are sleeping for seven hours or longer, but they're the lucky parents!
Still, every two-three hours is quite a lot when he's formula fed and eats a lot each time. I take it this is usual and not just a couple of days (ie. a growth spurt).
The sleep and the frequent feeding could be connected, sometimes babies who don't sleep well want to feed more often as comfort. Does he feed quickly and does he reflux back a bit, or does the whole feed usually stay down?
If he's fussing and appearing hungry he may actually be tired, and if he's over-tired because of too-short naps then he may want to feed more. If you always put him down to sleep you could try putting him in a sling or baby carrier when he starts to fuss. He may compalin more loudly at first, but if he's tired then a few minutes of walking around and singing to him should help him nod off. With the comfort of your body he's likely to stay asleep longer in the sling than in his pram or cot, as long as you keep your movements gentle.
Claire's also spot-on with the walks, the fresh air is really great for them and he may sleep longer in the pram if wheeled about.
When our little one was six weeks' old he was usually sleeping in two sections of three hours or a three and a four-hour at night. I put him down at around ten thirty and would follow him to bed half an hour later. He was also something of a napper in the day and I do need to encourage him (as with the sling, where he's snoozing away happily right now) to sleep for longer.
He'd also have his penultimate and last feeds quite close together, about 2 hours apart, so he went to bed with a really full tummy.
He very gradually began to sleep for longer stretches of time, although the last few days has also not managed more than 3 hours at a stretch.