Hi,

If I were you I would talk to a professional trainer to determine what kind of weight training you want to do and how it will work in with your schedule.  From my own experience, I work my upper body and core on the off days of running and then on the days of running I also do a few leg routines like squats, lunges, wall sits and calf raises.  That way I am working my legs all on the same days and my upper body and core on the other days.  By doing that I ensure that my legs get the rest they need between runs.  Just my 2 cents on that.  Hope that helps.

I believe weight lifting in between runs can help build your strength and endurance.  On my off days of running I like to do some other type of strength training, whether it is weights or just pilates, I find I am a lot stronger in my running when I do this.  Good luck to you.