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Depending on temperatures and the requirements of your tranny, you possibly could use the lighter oil. Best bet is to follow mfg specs. You might save some gas but I would guess the results would be hard to pin down. After all, your mileage probably varies by 1 or 2 mpg every tankful. How can you tell if you saved 1/2 to 1mpg by changing oil?
If you use a synthetic I think most applications would be safe.
The heavier oils work better for hot climates but syn doesn't care. I once got stuck in near zero temps with 140W in the gear box of a rice burner and man that tranny was hard to shift until it warmed up. the stick moved like it was plowing thru fudge. The lighter weight oil will work better in normal and low temps. Once again syn doesn't care.