What determines the right mattress: my weight or my sleeping position?

Both, but they determine different things. Your height and weight determine the firmness of your mattress: soft, medium, firm or extra firm. Your sleeping position determines which zoning and which comfort layer you need. Two people of the same weight therefore need the same firmness, but not necessarily the same mattress. A side sleeper needs a softer shoulder zone; a front sleeper needs a flatter, firmer surface.