It is very common. It happened to mine between 1 and 4 months old, too, and I've heard on here and from other mamas elsewhere about it happening with lots of other babies. I think it's part of baby "waking up" from the newborn period. Six weeks is the peak time for fussiness and disorganized behavior.
With a baby that's gaining weight appropriately and filling diapers, I wouldn't worry too much about it. If it drives you nuts, try something else for a time-- rocking, carrying around, setting baby down awhile, or whatever seems to work.
Lots of reason, I think, for fussy nursing: sometimes baby just wants to fall asleep, and wants to suck for that reason, and the milk flow upsets baby. A pacifier can help, or a finger to suck. Sometimes baby is annoyed by a slow letdown, or baby is unusually hungry because of a growth spurt, and the flow is slow and baby wants more. Frequently switching sides can help with this, as can having some patience and rolling with it for a few days until your supply catches up with baby's demand. Sometimes your letdown is too strong, and baby feels overwhelmed. Unlatching for a second and letting some milk run into a towel, and then relatching, can help a lot with this. Sometimes baby needs to burp, or needs to poop, or is experiencing acid reflux. In that case, taking a break and putting baby upright and attempting to burp baby might help.
Sometimes baby is overstimulated and tired from a long day, and really just needs to sleep-- they get so tired that they can't calm down and organize their attention enough to nurse well. Keeping the days quieter can help with this. That doesn't mean you have to sit home all day. But when you're out and around, keep baby close to you in a carrier, so that baby can get plenty of sleep during the day. Believe it or not, a peaceful day with lots of naps means better sleep at night, and less fussing in the evenings. Nurse frequently during the day, so that if baby doesn't nurse well in the evening, you're not so worried about overall intake.
When those fussy nursing sessions happen, try for a dark, quiet room. Try lying down with baby and nursing that way. Try to do whatever it is you do to help baby fall asleep. A nice walk outside, with baby in a carrier or in your arms, can work wonders if the weather allows. Even if it's chilly, you can put baby on your chest and button your coat around baby, and with a hat baby should be plenty warm. Even a car ride, if your baby falls asleep in the car, can help a lot.
My DD2 used to fuss like crazy at that age, in the evening, as if she were starving. I'd finally give up trying to nurse and give her to DH, and he'd rock her to sleep. She'd sleep an hour, wake up, and nurse like a champ. She was just too tired to organize her behavior enough to nurse well.