The guns were so small, that a single firing (so 14 guns shooting once simultaneously) could be loaded with a mass of balls that easily fit a man's pockets.
That being said, 14 four pound balls weigh 56 pounds (yes, you're welcome for me doing the difficult math), so they might fit in your pockets but you'll need a sturdy belt.
I'm glad I'm not the only one who went down that path...
I don't think that's what the author's intent might be. I believe the 4 pounder would be firing grape shot, not a large singular shot. So, the author is inducing you to picture that these, "cannons" shoot, not small bowling balls as you might imagine a normal cannonball to resemble, but a small sachet of marbles about the size of a juice box. One that fits in your pocket.
I guessed that it should have read "each of the balls".