I bought a house with a second story pre-fab fireplace surrounded by a stone hearth and faced with stone averaging 1 3/4" thick on the sides and front all the way to the ceiling which is vaulted. The fireplace is off center in the room so total height is about 8' on the left edge and 10' on the right. The weight of all this stone has bothered me ever since I decided I saw a dip in the floor by the fireplace associated with the warping of a doorway beside the fireplace in the same wall that backs the fireplace. When I finally looked at the structure downstairs under the fireplace I found a 2x4 wall over and along the basement posts supporting a beam under this wall. The wall downstairs is just beyond one edge of the fireplace, there is nothing under the center (except the floor joists) and the outside wall is three feet beyond the other end of the fireplace. So the fireplace is sitting on the second story floor joists which are 2x12's. I can't tell whether they are doubled or tripled under the fireplace without tearing out the first floor ceiling. I finally got a laser level and found that the entire house, upstairs and down, is admirably level except for 1/4" of 2nd story sag at the front of the hearth increasing to 5/8" at the back. The warped doorway is 18" from the right edge of the fireplace. We have been in the house four years and see zero increase in the doorway warpage and no other problems like cracked sheet rock. Is this much weight on a wood floor totally prohibited, or could it have been done right and produce a 5/8" sag? Is 5/8" a little or a lot? Do I need an engineer? The foundation walls are perfect and the builder is known for being a good one.
That stone produces a lot of weight. If a builder was to load a non-bearing wall on a joist, a sag could occur.
Although you may be in structural compliance with the weight of the stone and spans of the joist, a sag in the floor as you described is to be expected. You also mentioned that the sag has not increased in the 4 years you have lived there and I think that this is a good sign too.
If the house is fairly new, you live in area that is known for thorough building inspections, and the stone veneer is original to the house, that increases the chances that it was done properly.
You could remove the ceiling covering below the fireplace to expose the framing and then invite a structural engineer to inspect the work to determine if it was done properly.
Or you could continue to live with it, inspect it annually, and if no movement takes place, sit back and enjoy the fires.