Your cargo load limit in the Sportage is probably going to be your limiting factor. There should be a sticker on the driver's door jamb with numbers. Watch your hitch weight, too, load the trailer level, check the hitch weight with a bathroom scale, and don't go over 60 mph.
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I tow a Scout Lite with a Rav4 Hybrid (1750 lbs max towing) and it tows great. I don't do a lot of big mountains, though. My fully loaded trailer weighs 1550 lbs on a CAT scale. Hitch weight is generally around 168 lbs. I removed the lead-acid battery and put a LiFePO battery in the trailer. I only have a 5 lb. propane tank on the tongue.