I used to do something like this too, a few years back when I used a dedicated Win98se box as a router/proxy for sharing cable internet in the house. I used a combination of Deerfield's WinGate, and ICS. One of the nifty features of WinGate, is that it can re-direct requests to certain ports as a mini-HTTP-server. So I could share certain drives on my machine, map those as drive letters on the proxy machine, and make those available as HTTP servers using WinGate. It was lightweight, and worked out pretty well. Unfortunately, WinGate wasn't the most stable piece of work (or perhaps it was 98?), so the box had to be rebooted every few weeks. Stiil, it was a workable solution, and allowed me to share files over HTTP, with much less security risk to my main machine, if the web server was hacked into.
If you run Windows, there is a stripped-down version of IIS, called "PWS" (personal web server), that is available (still?). That solution would be free, but I wouldn't trust its security at all, knowing how many issues that IIS has had in the past.