1. If you run enough you will not gain any noticeable amount of bodyweight. Running is a very catabolic activity. Gaining muscle mass requires lots of calories, lots of protein. Most of your protein intake is going to be used just to maintain equilibrium.
2. You can gain strength without gaining mass. Happens all the time. You can gain strength through increase in muscle fiber size OR improvement in neuromuscular coordination.
3. Choose a goal. Do you want to look good, be strong, and also run? Or, do you want to run fast, be strgon, look good but lift in a way that helps your running?
If you want to focus on the running then lift in a way that will improve your running:
1. Reduced lifting volume. Increased lifting intensity.
2. Focused on lower body lifts for max strength and lower body lifts for max speed (plyos). Secondary are pushups/pullups or any sort of uppery body pressing.
Example:
1. Lift 1-2 times per week. Lift on your hard run days preferably hours after your hard run.
2. Do 1 plyometric or explosive lift. 3-5 sets. 3-5 reps.
3. Do 1 heavy lower body lift (squat or split squat aka lunge). Warm up, ramp up to a max lift of 3-5 reps.
4. Do supplemental upper body work. Pullups and Dips: 3-5 sets to max reps OR overhead pressing (I like the split jerk for this) plus pullups. Pullups are a great exercise because you will likely fail way before 10 reps if doing correct form.
Alan