Correlation between weightlifting and reduced injuries

I'm not sure that you'll find evidence of that.  Its a very subjective subject to try to study.

Even among coaches, its not clear whats best.  A couple of prominent local coaches debate the subject all the time.  One says it doesnt help, another does, especially for those over 40.

It probably comes down to what you think is best for you.  If you have significant strengthh imbalances, then yes, you probably would reduce your injury risk by evening out your strength. 

And yes, people tend to lose muscle as they age.  Weight work helps prevent this.

To the best of my knowledge, there is no independent research that proves weight lifting helps prevent swimming, biking, and/or running injuries.

Weight training to fix muscle imbalances could help as it reduces structural imbalances, which are what lead to injury. But that would be something done under the guidance of a professional who is able to identify structural imbalances and develop a plan to fix them.

But, I am not a professional, so take what I say with a grain of salt. Also, there is a
"Weight Training" forum on this site...you might get a better response there.

As for preventing injuries, make sure you do an adequate warmup/cooldown with your workouts. Stay well-hydrated, and eat properly before and afterwards. Don't increase volume too quickly; forget about speedwork for the time being. Foods that are high in antioxidants and other anti-inflammatory substances are good. Perhaps do an active stretching routine before your runs, and static stretching after or later in the evening. Ice baths after runs and other long/intense workouts are great. If you're a woman, be sure you're getting enough calcium, etc.

Just train smart and you'll be fine . Good luck !