rhltechie wrote:...does it matter what size the receiver opening is or anything of that sort as long as it will handle at least the weight of the TD?
Having covered the opening size, in the "anything of that sort" category there's the strength of the construction. Receivers with unnecessarily high capacity will generally be built stronger, and in some cases (including the case of the Cherokee) will mount differently. The stronger construction often means they are bulkier and usually means they are heavier.
The extra strength might matter to someone who wants a big margin of safety, and might make the hitch stiffer (which is generally good). The bulk may mean it hangs down more (which is bad in many cases). The mounting
may be more work.
I find the eTrailer site handy, because it shows a range of options for the selected vehicle, with photos. Most of the 2000 Cherokee choices are Class 3 units with 2" receiver openings.
If the vehicle is rated to tow more than the Class 2 limit (of 3500 lb) then getting a higher class of hitch might allow it to be used for more later; although that makes no difference to towing a teardrop, it might matter to the owner.
Since a 2000 Cherokee has a maximum rated towing capacity of 5000 lb with the 6-cylinder (if we can believe the Trailer Life guide) I wouldn't expect to find any Class 4 hitches for it, but a Class 3 could be useful.
Another short answer regarding whether "anything of that sort" matters might be "not as far as the teardrop is concerned".