I inherited some rolls which once belonged to the late Tony Clayton
(in the UK). These rolls are all safely and securely bound with Velcro
hook and loop fasteners in strips about 3/8 of an inch wide. The strips
hold the paper securely, are easy to release and fasten and, because
of their width and ease of handling, are less likely to damage a roll
than a thin rubber band.

I don't know if this is a product which can be bought in this form,
or if Tony had these made up, or cut from larger pieces of Velcro,
but I strongly recommend this approach for standard-size rolls. As
Velcro is double-ended, larger rolls would require longer strips and
I confess that I don't know how Velcro is purchased.

I just looked up Velcro and see that is is a British company, producing
loop-and-hook fasteners; I'm sure that this product, or something
similar, will be available in the US.

Greetings from the UK
Rowland Lee