I have been racing wheel to wheel for a bunch of years and whoever said it takes about a grand a weekend was right.
a typical weekend will cost me:

-about $250 entry fee for 2 sprint races.
-about $150-$200 for gas for my V-10 gas guzzler van
-most tracks I go to the hotels are about $65-$85 a nite for 2 nites.
-gas for the race car is about $100
-if you really want to be competitive you NEED fresh tires, about $700 for my Mustang

thats the big stuff then there is always food for me plus i usually pay for my cousin cause he comes to help and be my crew, I usually change my oil before each race, mobil 1, 7qts is about 50 bucks, then you cant get out of N.Y without payin at least $15 bucks in tolls each way because of the trailer's 2 extra axles.

so yea it runs into big bucks but I also run in a competitive class with cars that make big power and chew up parts, brakes tires and the such. it could be done a little cheaper but not much.