When was the last time you ran prior to your legs feeling heavy? Do you workout your legs often? Sometimes my legs feel "heavy" but I also weigh 230lbs and have 27in quads. I find the more I run the less I feel it.

Maybe lay off the weights and concentrate on calisthenics and swimming and running.....Until you feel comfortable running again....

Also being a runner in high school and college. but the more often you run the better your legs will feel. long distance running and heavy weight lifting do two different things to your legs. Although your legs maybe stronger from weight lifting they are not as agile they will be more for sprinting not distance running. Long distance running will tone your legs and slim them down. Thats why sprinters have more leg muscle than distance runners. The best thing to do for weight lifting is to do less weight but more reps that will be the closest simulation to distance running.