How much will I gain after 4 days of binge?

I’ve been 25 years binging so relax, 4 days is nothing. In 4 days your body doesn’t get destroyed if you get back on track.
As for why to stop, is simple, the consequences. If you maintain binging you will gain weight, lose health, be less attractive, be less happy or depressed and be worst at sports and have more injuries. Eventually you will also develop diabetes, cholesterol, high blood pressure and lots of no fun conditions.

If you didn't actually want to eat that much, it would be a really, really good idea to figure out why it happened, and make a plan to avoid repeats. (I know this isn't necessarily easy.) Other than that, just get back on your regular healthy routine, and everything will be fine, soon.

Theoretically, you could gain around 1.6 pounds** fat from this, but you probably won't. (For some people, it's normal for the body to up-regulate a little from *unusual* overeating, like make us warmer, raise resting heart rate a little, maybe make us move a little more in subtle (twitchy) ways, etc. It's extremely likely that you'd see a bigger scale jump than that at first, from extra sodium and sodium (which temporarily add water weight) and extra digestive system contents in the queue for eventual elimination.

At around your size (5'5", 128 pounds), I ate much more than that over a long weekend, not in my thinking a binge but a choice to live very indulgently for a few days and accept the consequences. Just for fun, I kept a pretty detailed record of what happened (estimating as best I could for some of the food, since it was restaurants and such), and wrote up the results as I returned to normal routine, and posted here:

https://community.myfitnesspal.com/en/discussion/10603949/big-overfeed-ruins-everything-nope

You might find it amusing.

If it were me, I'd be back on the scale the next day after all of this extra eating (I routinely weigh daily, first thing in the AM, and have for years). I don't freak out about daily weight changes - because I understand that quick scale changes are mostly water weight shifts and digestive contents variations - and I think it's fun and informative to see how my body handles unusual circumstances. Over time, approaching it that way has made me calmer about short-term scale results being pretty meaningless, and long term trends being the important thing for weight management. If you're very stressed by daily scale changes, that may not work for you. You know yourself best.

** (Four days times (3000 calories eaten minus 1600 calorie TDEE)) divided by roughly 3500 calories in a pound of body fat.

Best wishes!