Hi Kyle,
I'm doing it and it's hard. As you know, I'm training for my first triathlon (sprint tri) 2014 and Ironman 2015. With that being said, running, swimming and biking are *not* optional training sessions. So where in there does weight training come into play? I try to hit the weights 2-3x per week. It's nothing heavy but I do hit it hard enough to be sore.

My workout looks a little like this:

Workout 1: chest & tris
Workout 2: back & bis
Workout 3: shoulders and traps
Workout 4: legs
(repeat)

You may also want to look into supplementing with BCAA's if you're weight training.

I spend two days a week in the gym, but also do a lot at home (Ab Ripper X, resistance bands).

Day 1: legs, back, shoulders
Day 2: bis, tris, chest

I usually do abs at home, but when at the gym I'll do some weighted crunches/declines. Your core keeps everything straight, so be sure to not neglect!

Depending on my swim/bike/run, work, and home schedule (single dad), I hit the bands pretty hard at home when I need to. Just make sure you stretch properly, or you'll be miserable on your runs.

Kyle,
I consider myself a runner, primarily. But, I have more-or-less chronic plantar fasciitis, and about two years ago, I tore my ACL and had surgery. As I result, I have not been able to run all the time, so I have been supplementing with weight training.
I lifte 2-3, sometimes 4, times per week and I lift pretty heavy.
I think I can tell you this: the weight training does not really help your running. When you run, you get better at running, and, every day you spend at the gym lifting is a day you are not running. Moreover, the days after you lift your muscles are fatigued and sometimes sore, which impinges on your running. (Yes, even upper body soreness.) When I run the day after I squat with weights, I am REALLY slow.
All that said: Many runners now say that developing strength reduces likelihood of injury. Runners' World has a whole cross training workout for runners to do. You can Google it. I believe it does include push-ups and exercises like that, but it does not include weights.
If you are worried about detracting from your running, you might want to consider something like that.
And, I have come to really like the weight training. I enjoy the variety and it spares my body some pounding. I am in my 50s, so I need some sparing. Also, even though I am in my 50s, I have been able to achieve some muscle development -- at least, tone, maybe increased size. You don't develop muscle by running, really, and that is kinda cool.
I vary my work outs a bit. Mostly, I use the Starting Strength 5x5 program. It is simple, free-weight exercises, and you only do three, compound-movement exercises each time, which means you are done in about 45 minutes, usually.
Lately, I have begun following Kris Gethin's DTP training program. It is quite different from other programs and so is kinda fun.

I did Pilates twice a week during my last marathon training season. It was extremely helpful to my running. It really focused on core strengthening. I also like lunges & squats for strong quads and glutes. I use my arms, lats, and back a lot in running too. So I do upright rows in the prone position, flys, push ups, planks, walking planks. I run 5 days a week & strength train 4. I only use 8 or 10 lb weights.