Hard to answer questions like this . . . there's really no "question," more of a request to transcribe an awful lot of information in a generically accessible way.
I'll try to keep it short.
Two things limit how "beefy" of a tire you can add.
First are parts of the jeep body-- mainly the fender flares and pinch seams. The taller the tire, the more it comes in contact with these items. You fix this by either getting a lift or by trimming the affected pieces.
Second is the backspacing on your wheels--which is essentially how deep your wheel would be if you turned it on its face so it looked like a bowl. Low backspacing means the bottom of the bowl contours up toward the top of the bowl. The result when you mount it on the jeep is that it widens the stance and sits the tires farther out. High backspacing means the bottom of the bowl is close to the ground, meaning that when you mount it on the jeep in narrows the stance and pulls the tires inward.
The wider the tire, the lower the backspacing you need. If you put a wide tire on a wheel with high backspacing, the tire rubs some of the interior components inside your wheel well.
33s are short enough to fit on a JK without a lift, though if you go offroad and "flex" the tires up and down over uneven terrain, you'll usually hit the fender flares or pinch seam. So, again, you should get a lift or do some trimming to compensate if you plan on going offroad with 33s.
Stock wheels have relatively high backspacing. This means wide tires (11"+) usually don't fit. You can fix this by getting two sets of SpiderTrax spacers ($200) to push the stock wheels outward (simulating low backspacing), or by just getting new wheels that have lower backspacing to begin with.