J.F.
Well yes 7 weeks is a bit too young to expect good sleep from him, but it sounds like he is harder than it should be.
I would say that my first daughter LIVED in her swing at least during the day! The docs said that was fine and she would out grow it and she did!
Now she is a great sleeper.
I would give it some time, but you can do some other things and see if they work.
First I would say always try and put him to sleep in his room. Make it dark and have white noise! In the winter we use humidifiers and in the summer we use a fan! That trick alone has gotten us 2 great sleepers. Also make sure the temp is mild.
I also rocked my babies while feeding. They fall asleep in my arms and then off to the crib.
Of course in the beginning it takes practice! Sometimes you only get 5 minutes before they are back up, but you just try try try again! After awhile we got longer stretches and now my 2 year old and 10 months old take naps and got to bed like clockwork!
Another thing to try is baby wearing... google it. Both my girls were fussy babies and loved being held and this too helped them get over that phase.
All I can really say is good luck. The first 1-5 months for me were not the funnest of my life. But man once they start to sleep your whole word changes :) Hang in there and this too shall pass!