Cheryl in Kenton, Manitoba is worried about breaking tiles under her wood stove. Actually Cheryl, the tile itself can easily carry the weight, as long as it is not a pointed contact. If the feet are bent and do touch on one corner, put a metal plate about 2 inches square under the feet to spread the weight out.
You can also break the tile if they are not solidly supported underneath. A flexible floor will break tiles as will missing thinset mortar that leaves a hollow spot under the foot of the stove.
So, from the bottom up: a solid base, complete mortar under the tile and a weight spreader for point loads and you do not have to worry about that very heavy stove breaking tiles.