Run more miles total.
Run a longer long run.
Run faster 2-3 times a week.
You are never genetically screwed.
I've seen a 6 foot 225lb dude run a sub 13:00 2 mile on 10-15 miles of a running per week.
So...
#1: One day, run long. How long? Longer than you are currently running. Increase 1 mile per week until you are running 8-10 miles in a single run.
#2: Twice per week run fast. How Fast? I don't care. One day make it really fast. 400s, 800s plus some short 50-100m all out sprints at the end. How many? I don't care. 2 miles worth is a good number to start with. So 8 x 400m or 4 x 800m. One day make it hard sustained run. How long? I don't care, at least a mile. How fast? Faster than a normal run. Slower than a sprint.
#3: Run more often. How often? I don't care. More than you are now. 5 days week. 6 days a week. At least take one day completely off. Drink beer. Rest. Do other recreational activities.
So...
Sunday: Long Run. Up to 8-10 miles
Monday: Easy run 4-6 mi
Tuesday: Track work. 400s. 800s. short sprints
Wednesday: OFF
Thursday: Hard run. 2-3 miles. short sprints
Friday: Easy run 4-6 mi
Saturday: Off
Ideally: Lift weights 1-2 times a week. Keep it simple. Squats. Bench Press. Deadlift. Pullups. 2-3 sets. 10-15 reps. You seem to lack conditioning. Don't focus too much on how much weight you are lifting. Just lift focusing on form and repetition right now.
So run 25-40 miles per week using the above schedule. Lift twice a week. Focus on getting faster Tuesday. Run fast. Focus on running harder longer Thursday. Focus on running longer slower Sunday.
Alan