Mischarging and miscategorizing with first class mail

I have an ecommerce store selling tangible goods. Most of my products are too large for first class mail and ship in packages – either by USPS ground or priority mail. I recently started offering the ability to purchase samples. Those are light enough and go out in smaller envelopes so first class mail is the most appropriate and cost effective shipping rate. When I enable first class mail however, it lists first class mail as an option even for large packages that should not be sent via first class mail and it undercharges- of course people choose that option because it’s by far the least expensive. If I disable first class mail, it means people are paying like $5 in shipping for a letter that only costs about $1. Please advise.