I've seen some people use their belts as tight as they can physically cinch it while others have recommended only a 'snugness' to the belt. What factors are important to keep in mind when tightening a belt for a heavy compound lift?
The biggest factor to keep in mind is that a belt is for your abs to brace against, not to support your lower back. Your spine is kept stable by the additional intra-abdominal pressure (IAP) you can generate by bracing against the belt.
My personal approach is to pull it just about as tight as it can comfortably go and then back it off another notch. This usually ends up with me being able to squeeze my hand in between my belt and abs; although, not comfortably. After that, I brace using a cue I learnt from Chris Duffin, imagining the core as a cylinder.
If the belt is too loose, it isn't going to add to the pressure I can already generate in my core. If the belt is too tight, I also can't expand my core as much as possible to create additional pressure; it is going to inhibit me. Again, if the belt's tightness impedes your ability to brace your core, it is too tight. I will usually be a bit tighter on squats than I will on deadlifts just so that I can get my body in a proper position.
There are many individuals at gyms that use powerlifting belts without knowing about the concept of core bracing. These may be the individuals you've seen tightening the belt as tight as physically possible (to the point of interfering with proper breathing). My opinion is that at this point, the individual is using the belt as a crutch for a weak lower back.
Conversely, there are individuals that crank the belt down as tight as possible, they have a fantastic knowledge of how to use it, and that is just the method that works best for them.
Belts seem to be a rather personal thing. Lots of people have their own methods. I would suggest playing around and seeing what works best for you. Again, @DeeV had some great points on my equipment question and I highly suggest checking out the Belt Bible by Greg Nuckols.
I always tighten my belt that I can stick 1 or 2 fingers between belt and body. As commented opinions are divided about it, but all agree it works.
As by the link in the comment, first few months dont use a belt, as your body wont train some muscles as it should (with deadlifting your back wont know how to keep itself steady if you ever lift without a belt).
The most important point is, is that the belt shouldnt feel unpleasant if you are under tension. If you pull it too tight it might 'cut' into your gut. The best tactic is to try with a moderate weight you are familiar and try the different tightnesses.
Research: my own, some friends from the gym and my bodybuilder coach.