I do something like this, but it is for longer term rewards than weekly things. For example, for every pound I lose, I am setting aside $5 (like you). Then, when I get to my goal of 102 pounds, I will have $510 to spend on a brand new wardrobe. I'm not frustrated by week-to-week fluctuations.
In the meantime, I had a big reward at 26 pounds (a new bike), and I'm planning a big one for 50 and 75. Yes, it takes a little longer to see the benefits, but I'm not a slave to the scale. It sort of motivates me to work harder.
One thing I did do, when I first started exercising, was give myself money for every day I went to the gym. Now I'm in a routine and don't need the reward, but for the first couple of months, I lived for blowing that money on Amazon at the end of the week!
Going to Colorado Goal: 216
No Longer Obese Goal!: 202