With more weight you shouldnt need a tie down. Inside the Everlast I have is lots and lots of cotton. The bag is strong enough that you could take some in and substitute sand. Its more work, but I would put the sand in the bottom, then the packing(cotton) on top. That way its harder for it to swing out. Also sand is a little less forgiving and you probably dont want to punch it.
You can by sand in 20 pound bags at Lowes or home Depot. Drop them in a trash bag and go for it. I wouldnt add too much though.
"When I let Go of who I am, I become who I might be."