Long-time librarian. Normally when rolling shelving is apt to tip, the problem is weight distribution. Binders and baskets are going to be lighter than bound books (well, unless you store bowling balls in the baskets.) Rearrange the shelves so that the heaviest items are on the bottom and the lightest on top. You could also put some clay tiles flat in the bottom of the basket to make it heavier.
Also, since they are prone to tipping, adding elastic lines to the front of the shelves about 3 inches up from the bottom will save cleanup if they do tip a bit when moved (same principle used on boats, but stretch gives you more flexibility than hard rails). You can drill holes through the outer sides about an inch back from the front edge, then sew the elastic securely to a flat shank button that is larger than the hole. Sew the second one on with the line in place and the elastic stretched; it will pop tightly into place once you release the tension. Alternatively, you can use wider elastic, fold the ends under, and put a screw into the folded end on the face of the bookshelf side, but depending on what the shelf is made of, that method may not work as well.