Being a tightwad (frugal person, cheapskate, spendthrift, etc) has a purpose. In my case, I am trying to save money so that I can pay of debt and rebuild savings. Tighwaddery also has another purpose. It allows you to save money so that you have money on hand when a good deal comes up.
For example, some people might find that they get a better deal on a car if they negotiate with cash. Or, if canned goods are on sale for 10 cents each, if you have cash on hand, you can stock up on a bunch.
My gym membership expires this month. They are offering a promotion where if you pay/renew for the whole year, then they will sell you the membership for halfprice: 12.50/month vs 25/month. The catch is that you have to pay all at once.
I don't have $125 laying around, but I will try to find money in the budget as this will allow me to save $125 down the road.