Correct paper/type selected in the Printing Preferences dialogue boxes?
Printing using the plain paper setting will reduce the amount of ink being laid down by the printer.Proofing paper is designed mainly for checking position and layout of an image rather than colour balance so it's unlikely you'll find a profile for it. If you want to print quality A3 then you need to use a quality paper. However if you need to print on your proof paper try one of the standard setting , Gloss , Matte . However be aware proof paper may not have the same charecteristics as photo quality ink jet paper
Don't the paper manufacturers have them for an assortment of printers? If you can't find a profile for yours specifically, try the profile for another Canon printer that uses the same inkset. Or just spend some time (and ink + paper!) creating your own.
TBH, it's up to the paper manufacturers to make sure their customers can get decent results from any printer rather than the other way round. As I said, a couple of sheets of paper cut down to small sizes and a little experimentation should get you the results you want if you can't find a premade profile for that printer/paper combination.