Riddle me this. What causes my engine to surge a bit at low speeds but only when the heat/a.c. is on, and makes the belt squeal while turning, but only when the blower motor is running high?

I'd say your fan kicking on. Would only make sense.
Now the squealing sound.... first check your belt tension (engine off obviously lol)
Second... could be your fan clutch starting to go.

I'm cleaning the throttle body tonight. I'l check the belt. I'm planning on getting a new one soon. If it keeps up I'll replace the fan clutch. See what happens.

I'm suspecting that it's not the belt. Doesn't mean it may not be worn or not properly adjusted. But there's very little movement from the clutch on the a/c compressor when you engage it. So don't think the belt would cause that. And if the root cause was the belt, I'd think you'd hear it regardless of whether or not the compressor was engaged.
I think it may be more likely to be either the fan clutch or possibly the a/c clutch. Not sure exactly why it would only occur when on full/high blower setting.
Does the sound come from inside the engine bay or from inside the Jeep?

definitely engine. I'm really thinking it's the fan clutch. I haven't run the ac, so idk if it's dry. At 244000 miles, I'm sure everything along the belt will be new by the end of the year. Belt is tight, but I'm still planning a replacement.

Anyone have a recommndation for a replacement?

New Belt: 180-200 lbs
Used Belt: 140-160 lbs?

New Belt: 180-200 lbs
Used Belt: 140-160 lb

I should say to me it feels tight, though I'm not 100% sure how to proper check the tension. I've heard it shouldn't flex more than 90°?

NAPA, E-bay, Amazon...

The surge when idling could be the A/C kicking on, possibly a bad a/c clutch or a weak alternator.
Have you checked you PS level? Low PS fluid when turning can sound a lot like a squealy belt.

I love the "gatorback" belts - formerly of Goodyear, now they're called continental something or other. I had belt noise on both my TJ and XJ and putting a gatorback belt put a complete end to it.
I'll see if I can dig the part number up.

Often the A/C will kick on if you have the selector set to any "defrost" setting. I know for sure this was true for 97+ years.
So it's not uncommon for people to think that "it can't possibly be my A/C, it was off" when actually it might not have been.
​​​​​​​Just food for thought.

I'll go get the alternator checked today and do some ac testing. I did not know it kicked on while defrosting. Never would have thought it. This is the firs car I've had where it's not just a button, so being on the end of the heat section never would have made me think about it!

I had never thought of it myself, but I was reading through the owners manual on my TJ many years ago and came across it. It makes sense though, the A/C really just takes humidity out of the air... when it's blowing cold it makes the air colder, but when blowing hot it helps to clear the humidity that's fogging up the window.
In my family car (2010 corolla), the windows fog up super quickly when running the heat, so I constantly have to flip it defrost or hit the A/C button to clear it up. When you switch to defrost it automatically turns the A/C off (the light on the button), as I'm assuming that the defrost uses the A/C at it's own whim.

The gatorback is a "continental elite", you know it's the one if the ribs have a slanted angle across. It wasn't clear what size a 2000 cherokee takes, but it should be easy enough to figure out with the length and number of 'ribs'.

I know what you're talking about now! My BMW has continental on it. Forgot thats what the mechanic put on.
I tested the ac and it does the same thing as the defrost. Hard idle and squeal. I' not too concrned now that I know, but I'll definitey replace the compresser and belt this spring. Thanks for the help!