If you could print very light lines and the costs were very low, I'd be interested. As someone who works a lot with handwritten formulas and pencil & paper sketches, I'm constantly annoyed by how strongly lines and squares are printed on paper. It's distracting and there is no need for it.
Print in lighter shades of grey.
As someone who shares the same frustration with normal graph paper, check out a Rhodia Dot Pad.