I've done alot of reseach on this one, and the lightest tires you can buy are:
235/40/18 Toyo T1S - 22.9lb
235/40/18 Continental Contisport Contact - 22lb
225/45/18 Continental Contisport Contact - 23lb
235/40/18 Pirelli PZero Nero - 22lb (and these are uni-directional)
Note: per
http://www.miata.net/garage/tirecalc.html, 235/40/18 is only a hair smaller than our stock size, so the effect on the speedo is next to none. Also not all tires come in all sizes so i didn't my best to match to our stock size. 235/40 and 245/40 are both damn close to our stock 225/40/18
for the record, the weights of some popular heavier tires
RE040 225/24/18 - 26lb
Bridgestone SO-3 225/45/18 - 25lb
BFG gforce 225/45/18 - 24.76lb
AVS 100 225/45/18 - 24.55lb
Kumho 712 245/40/18 - 27lb