Look inside all the cabinets, there might be a sticker on the door with the GVWR and an estimate of the dry weight or some other indication of CCC (cargo carrying capacity). Possibly also the manual or the manufacturer.
The empty weight of the trailer, on that sticker, will be called UVW or Unit Vehicle Weight. It is supposed to be within 5% of actual weight. GVWR is the maximum weight the trailer is designed to carry with the axles and tires installed.