My only opinion on this is as follows:
Do not vary from the Owners manual on recommended oil.
These engines have such tight exacting tolerances higher viscosity (thickness) of an oil will not flow properly.
Too low of a viscosity (thickness) will not lubricate properly. Both cases are bad for the long term health of the engine.
Most of the wear on an engine occurs on cold start ups until the oil begins to flow.
Obviously with a 5W, any remaining oil on the cylinder walls will be 5W when the engine cools off.
That is where the viscosity is critical, especially during cold weather. Not too heavy to impede the start up but enough to protect the engine during those early couple seconds of start up.
The Engineers come up with what best serves the particular engine. I would rather not tinker with that.
Basically oil these days are for most vehicles all season. In the old days I'd have to change winter/summer. But again using a 10-30,10-40, or a 20-50 was the norm.
That is the problem with some oil change places. They will make do with what they have. There is also an approved list of oil for the Cherokee the last I heard.
The oil filter is also specific even though one from a particular Grand Cherokee year will fit. The only problem is that it will produce low oil pressure..........
That is one of the reasons I take it to the dealer for oil changes 2x a year. Costs a bit more, they have the correct oil and filters, but they also run codes for me and check if the tires need to be rotated.