Swamping a barrel removes steel. No way that can increase weight.
Swamping improves hold and balance and even the graceful lines of a long rifle.
But, with no experience, cutting your barrel channel for a swam could be very challenging. You should join the National Muzzle Loading Rifle Association (NMLRA) and buy some of the books on the subject advertised in their magazine, Muzzle Blasts.
You have a big project ahead of you.
Remember, it is very easy to turn $1,000.00 worth of parts into a $200.00 rifle.