Hi Andrew, and welcome!
The first thing to be sure of, is that your belt is being joined properly. Little fixtures/jigs can be made to ensure alignment, but all the problems I've had with belting in the past have been unrelated to the alignment of the belt ends. I had a hard time with this myself, when I was starting out. It was like no matter what I tried, the belt would snap. What kept getting me was my ignorance of the subtleties of the belting material. Of course it makes sense that if you don't get the material hot enough, it won't bond together... but it may be less obvious that if you get it too hot, it also will not hold very well. If memory serves, 200 degrees C is the correct temperature (but that may vary for belts from different manufacturers). I've found that a good rule of thumb is to heat until it just melts, but no further. Make sure that the belt ends are kept pushed firmly together until the material is hardened up... I give it a good several minutes, personally. Where the seam mushrooms out, just trim that off with a sharp razor. Lastly, it is really important to note that the material can apparently take up to several days (depending on the diameter of the belt material, of course) to fully cure after it is melted and joined. I had a hard time believing this myself, but sure enough it seems to make a big difference.
With that out of the way, even if you're running your belt a bit too tight and making really heavy cuts, the belt still shouldn't break. The belt really doesn't need to be very tight. With the belt removed, your lathe spindle should spin with a silky smooth, consistent feel, and the only resistance you should feel is the heft of the pulley. If the spindle is smooth and free, much belt tension shouldn't be required at all. The way belt tension is measured is by the belt deflection between two points. But everyone's setup is different, with the distance between those two points being variable. Belts from different manufacturers do have different grip too, to further confuse things. The genuine Swiss green belting is more pliable and has more grip than the green Chinese stuff (I use the Chinese stuff now, but have used the Swiss stuff in the past), the Chinese stuff needs a bit more tension to have the same grip. Aim for something a bit on the loose side, then adjust the tension to increase it as you work, if you find that it slips. On my own setup, I have the belts (motor to countershaft, and countershaft to lathe spindle) set loose enough that they can be "run over" the edges of the pulleys to quickly remove the belts when work is done. They have to stretch a bit when running over the pulley edges, but do so easily and the fused joints handle it just fine.
That is a brain dump of my own experience on the subject, if any of the professionals chime in with different opinions, you should probably take their advise over mine.