Use a cloth bag for heavy items, the plastic/paper bags are not really designed for multiple reuse, they are more so for when you have more items than the cloth bags you brought with you. Plus the cloth bags have larger handles meaning can carry heavy items on shoulder which is more practical.
I do buy one paper one every week as excellent for putting the recycling in, then can be tossed in the recycle bin, rather than the hassle of emptying a box or plastic bag.