Weights are for Strength training. They are not an endurance tool. If you want endurance and increased efficiency in O2 uptake and aerobic markers - Run, Cycle, Jump Rope, Swing KBs, Snatch KBs, Clean and Jerk KBs, Jerk KBs etc...
Strength helps endurance - Endurance will not help strength. Anaerobic improvements will improve aerobic - Improvements in aerobic will not improve anaerobic.
Use the right tool for the job. 20 reps of squats for example compared with 10,000 steps during a 5K race is nothing. It will not improve the O2 uptake specific to the task of the run. On the other hand - increased strength will allow fewer muscle fibers to be recruited for each step and leave more in reserve and less demand on the O2 uptake.
Power - is improved through strength. Even endurance events are power events - how fast can you move X amount of weight (even if that is your body weight) in what time. Well if you are stronger and able to move X amount of weight with more force (ie. faster) then you go....ummm.... Faster.
Strength train to get stronger - then go use your strength in your sport skill practice.