Why does an 8 point DFT behave differently from a 16 point?
Your sin frequency is 50 Hz, but in your 16 point DFT there is no 50 Hz bin.  There is a 0 Hz bin and a 100 Hz bin, and you can see that some of the signal power goes into both of them.  This is a non-ideal way of capturing a 50 Hz tone.

The 8 point DFT has a 50 Hz bin, and you can see that it captures almost all of the signal power.