Hi I’ve been looking around everywhere for some sort of answer to a question but can’t find anything. 
I’m looking to weld my ae71’s diff but can’t find anything hinting towards the strength of the axles or anything related. Surely the car is light enough that just driving around won’t snap axles?

If you give it a hard enough time I'm sure you will.  You're relying on making one rear wheel skid on the tarmac every time you turn the steering wheel, so the stress depends on how much grip the tyres have.

Don't weld the teeth together in the diff, fill a pair of teeth on either side of a spider gear so the gear has a little movement but can't move past that one tooth. That makes the car turn in much better than having it plough straight ahead with no play between the rear wheels at all. Eventually you will break a spider gear I expect, although we twisted axles in the Celica rally car.

"Just driving around" with a welded diff is a serious pain in the arse.  

It really isn't worth it believe me

I broke a 55 axle once "just driving around". Weldies put so much strain on the whole drive train, not just the axles. If the axles were somehow super strength, you'll just end up blowing out spider gears.... or maybe a gearbox instead. Yep, I've done both of those too. Haven't run a weldy since. And you know what... I now put 180rwkw through a stock ke55 diff and life is peachy. Just my 2c.