It should be pretty close to the dry weight plus that of any water, etc you put in it along with any additional accessories. Any carpet protection cling film, tape and cardboard will not add much measurable weight.
The 1800 is a dual axle which allows you to load it from its dry/empty weight of 3660 lb to its max of 7000 lbs gross giving it a 3340 lb load capacity while the 1700 is a single axle trailer that is 3010 lbs empty and 3700 gross giving it a 690 lb load capacity.
Filling either with propane uses 40 lbs of that load capacity and the 31 gallons of water consumes another 248 lbs so 288 lbs load capacity will be consumed on either before adding your stuff leaving you with only 402 lbs of weight capacity remaining on the 1700 after water and propane is added while on the 1800 it will have 3052 lbs of weight capacity remaining. Food, clothing, blankets, pots, pans, dishes, camping gear, accessories, etc add weight very quickly so the 1700 would be best for couples who travel very light.
Shipping weights really would only apply to trailers that are loaded on a flatbed tractor trailer or train car potentially on cradles with the wheels removed to keep the load height lower.
2001 Winnebago Adventurer WFG35U