I just started racing these last year on dirt and I can run you through some of my weekly costs. As you mentioned, car purchase is anywhere from 4500-10k (I payed around 6k for mine). Bought a set of dirt tires for it (about $450-these things last 1-2 seasons), and some springs (new-about $65 a piece x2= $130). Bought a trailer to tow it in ($3k). New racing suit ($400), hans device ($700), helmet ($350), gloves (30), shoes ($40). That pretty much covered my initial expenses ($11k).
Asphalt tires are gonna end up costing more in the long run because they have to be camber cut to be competitive, so that adds to the per tire price, and also cuts down on tire life. Top teams are buying new tires almost every race, where the budget racers are getting probably 5-7 races on a set.
Beyond that, racing on an almost weekly basis isn't all that expensive unless you have to repair stuff. My local track is fairly close, so gas to/from the track isn't very much. Pit passes run about $25/person (me and my wife), and last place pays out a "free" pit pass for the track, so after the first race, it only costs us 1 pit pass/race. Couple gallons of gas for the racecar each race also.
I can't comment on engine rebuilds prices yet, as I haven't had to do one, but the engines seems to last 1-2 seasons before needing a rebuild if you take care of them (depending on how many races you do). The main this is making sure these things stay cool.