All the times I've tweaked something have had common factors.
1) I go for more weight after a PR.
My old strength/conditioning coach pointed this out. Once you hit a weight that is a record (currently, not last year or when you were 18), stop. You can come back again next week to improve on that. This applies to a 1rm or a rep record.
Example: I don't remember the weight but it was around 215#. I hit 10 the week prior, was going for 11 that week. I reached 11, felt good, tried to squeeze out 12....strained my neck.
2) Half ass warm up.
If your lifting near-maximal weight, you need to prime your body. Your warm up should not be apart of your workout. Get the blood flowing, open up your hips/shoulders/etc, then get after it.
Example: My max was around 500# on deadlift. I was going for a triple with 440# or something like that. I was in a rush, didn't stick to my warm-up. Tweaked my trap on the 2nd rep with relatively 'light' weight.
3) Having a weak neck.
What I mean is recognize your weakness and fix them. The most common tweaks I've had are all in the neck/trap area. I started specifically targeting my neck when doing accessory work and I haven't hurt it since....accept when I've ignored the first two rules.
4) If you can't lift something with perfect form, you can't lift it. Put it down, bail out, or have your spotter take it.
Following these rules will make you chance of injury GREATLY decrease. Good luck on your journey. It's never too late to get stronger.
Also, check out West Side for Skinny Bastards. Following this template has made me the strongest I've ever been.