IF the tile was properly installed it shouldn't break, BUT if you are still concerned, install a layer of 1-1/8" Sturd-i-floor under the washer (and dryer, to match heights). You can secure it with brackets to studs in the wall behind the washer or simply use some adhesive in a few spots. Be sure to put the washer on it after applying adhesive so that it will squish down, to avoid air voids. For uneven tile you may need to install a THIN layer of something such as what is used under laminate floors, to prevent possible hum from vibrations in the sturdifloor (VERY UNLIKELY, as it is 1-1/6" thick). I'm giving you these instructions to be on the safe side to avoid complications--not saying that anything I mentioned is likely.