For the sake of curiosity, why not a 225/50? More potential lateral grip correct? Or is the downside to that the requirement of an 8 inch wide rim? Or could you fit a 225 on a 7.5inch rim?17x7.5" rims are a good compromise. You can find light 17" rims fairly easily and somewhat inexpensively. Tralkites, Advanti and Konig are good ones to look at. The 7.5" Traklites are just a bit over 15 lbs each. Look at wheels for the 3rd generation Miata, 2006-2015 for a wider selection. Check out Goodwin Racing for more choices.
Better tires sizes are available for 17" rims too. 205/50s on 7.5" rims is a good choice for performance.