Does the backing of sandpaper matter?

Yes — it decides where the abrasive can be used at all: paper is cheap and tears, film is thin and even for fine finishing, and cloth survives belts, drums and anything that has to bend.

Grit gets all the attention. The backing decides where a disc or a sheet can be used at all.

Paper

Cheap, made in every grit, and it tears. Weights are given letters, lighter for hand sheets and heavier for machine discs. It is the right answer for flat work with a random orbit sander and the wrong one anywhere the abrasive has to wrap around a shape.

Film

A thin polyester backing of uniform thickness, so the grit sits at a consistent height and the scratch pattern is more even. That matters at fine grits, where an uneven backing shows as isolated deeper scratches. It does not tear, and it costs more.

Cloth

Woven, flexible and by far the toughest. It is what belts, drum sleeves and flap wheels are made from, because all of those bend around something and take heat.

Mesh

An open weave rather than a backing with holes punched in it. Extraction pulls dust through the whole face, so it clogs far less than paper on the same job.

What to take from this

For finishing flat surfaces, film at fine grits repays the price. For anything that flexes or runs hot, cloth. For resinous timber and paint, mesh at any grit.