To get faster, you must train faster.
Weight training has it's place, but is nearly out of the question when speaking in terms of endurance running. Reading the post, it seems as if you want to be able to develop a faster pace during your runs.
Again, to increase speed, increase your training speed. There really isn't much else you need to do. You can get fancy and do lots of leg work.... but where does that pay off? The fancy leg exercises! Not the run times. To make it simple, but a bit general, look at things as either AEROBIC or ANEROBIC. Running distances where you can't hold your breath the entire time(lol), aerobic. Squats, lunges, high jumps, short sprints, anaerobic.
Now don't get me wrong, I do bodyweight squats all the time, and I love circuit training with lunges, high jumps, ect. Great for leg power and endurance. Not necessarily so for running.
What I currently do to increase my pace is run 1/2mile (2 laps) fast paces at the track. 100 meter sprints don't hurt, but if you want to run faster LONGER, 100 meter sprints will sell your body short.
As an example, my pace right now is approaching 21 minutes for the 3 mile. So what I have been doing on my speed days is 1/2 mile runs at around a 6 minute pace. Do at least four of these, while keeping in mind that you don't want to be TOTALLY exhausted after each interval... out of breath, absolutely, but it is not a sprint. You want to do this twice a week, IN MY OPINION.
2 lap fast paces I think are ideal for 5K or the like distances, but many professionals point towards 1 fast pace lap intervals, with shorter rest times. Check out Hal Hignon 5K training for a great template of how to increase run speed.
Just remember: You don't NEED to get fancy... to run faster, train faster