USPS 1st class vs. parcel post

[jmrcrp]

I want to ship my products first class if total weight is under 13 oz, but ship parcel post if over 13 oz.  (this is the USPS rates - first class can't be over 13 oz.)   If I choose both of those options when I set up the shipment method, will it automatically show only the parcel post choice to the customer if the weight is over 13 oz.?  Or will it still show both shipment methods?  I can't have the customer choosing first class for a 2 lb. package, it has to be shipped parcel post.

Thanks for any help you can give.