Strength Work (Weights) while Training for Marathon???

 So now that I've reached my weight loss goal (yea) I've set a "new" goal, I would like to Run a Marathon!  I plan on doing a 5K Turkey Trot this Thursday (Thanksgiving Day) and will likely try a 1/2 Marathon first.  

Lately, I've been doing about 3 to 3.5 miles generally around 30 mins.  I've started reading up on Training for a Marathon and will begin on a 16 to 18 week training plan.

My question:  What about Strength Work or Weights, while I am doing the Marathon Training?  

I've really come to enjoy my morning routine of about 30 mins of cardio followed by 30 - 40 mins of strength (weight) work.  How do I work the weight work, especially for my upper body, when I am focusing on building up my distance and endurance?

Any suggestions or resources? 

Thanks!

 As the miles creep up, I had to really scale back my lifting.  First, no leg work at all - 25+ miles a week is plenty of work on the for sure.  I just about halved my routine, and mainly focused on the large muscle groups (back, chest, Shoulders, abs) and just did minor isolation work on the arms.  

As an example, on chest/tri day,  normally I would do 3 sets of 10-12 for fly's, incline flys, bench press, pushups, skullcrushers, dips and dumbell kickbacks.  Plus tons of abs.  As the miles crept up, I needed to halve it, and really only do 1 tricep exercise.  Even with that, by the time my long runs were pushing 17 or 18, I was completely wiped at the end of the week - and several weeks I needed to take 3 days off completely to recover.  It worked for me though.. :)  

I think for me the advice is keep doing workouts you love, with the same intensity but less volume, and don't be afraid to take real rest days as much as needed.  And if you do skip a weight training session, don't fret it, and don't try to make it up.  Just move along.  

while training for my first marathon i scaled back lifting on legs but not upper body.  i'm training for my 2nd now and i've actually increased my lifting and am increasing my legs workouts.  i've found great results between that and limiting my running to only 3 days a week (one speed day, one medium tempo run, and one long steady run).  the improvements have been great and my overuse injuries haven't cropped up as much as the last time.

I find whenever I up my strength workouts, my run gets faster. I also never run 2 days in a row or more than 3-4x a week.

I was told by a famous foot doctor that body parts wear out and everyone should ration their running. Works for me!