Tape measure spiral. The upper part expands more than the lower one I have a tape measure at my home and while I was trying to swing it like a spring I notice that the lower part of the take measure is wound tightly and extends less compared to the upper parts. I want to know the reason for this. Shouldn't tension remain more or less constant in the tape measure due to it's extremely small mass.
Also if it is relevant the take measure is kept coiled for most of the time

 A: yes it is relevant that it was kept coiled for most of the time.
Because of the material the tape is made from (plastic coated perhaps)   it will form or gain a memory . because the inner  side of the tape is wrapped  tighter it is affected more than the outer side of the tape, "ie" different circumference, and as the coils get larger there is lesser  change to the molecules or structure of the material. 
At the bottom of the tape the weight reduces so it has less chance of straightening. If you hold the tape by the curly end  it will straighten out more quickly due to the weight of the rest of the tape, and if you apply a little heat with hair dryer it more likely straighten quicker, because the heat will relax the material structure.
A: Ok, here is my guess.
When you wind the tape up, as you wrap it around and around, the inner core receives some of the tension from each turn of the tape, so the inner core has the highest tension by the time you are finished wrapping, especially if it is a long tape.
This is then reflected in the behavior of the tape when you release it, as shown in your picture.
A: The bottom is inside of the wind.  I was and is more bent.  
Tension is relative. The top has twice as much tension as the bottom.
