Don't confuse the various flavors of first class mail or other USPS services. The best way to get the correct info is to visit the USPS website. Just google your question to find the answer quickly.
You've been thinking your 8 oz package qualifies as what USPS calls a "large envelope." Here are the requirements for large envelopes, aka flats:
https://pe.usps.com/businessmail101?ViewName=Flats To summarize, your package does
not qualify as a large envelope because it is over 3/4" thick.
Instead, it qualifies as a first class parcel --
https://pe.usps.com/businessmail101?ViewName=Parcels
If a postal worker accepts a package as a large envelope when it does not actually qualify as such, and this does sometimes happen, be aware that the package may be detected in transit as having insufficient postage. Like other carriers, USPS is increasingly using automated equipment to detect whether a package meets requirements or not, so it's more likely you'll encounter this nowadays than in the past. If your package has insufficient postage and you are a regular USPS retail customer, your customer will have to pay the difference and that usually means you'll have to deal with an unhappy customer. It is best to get it right rather than hope your oversize package flies under the radar.
Here's the easiest way to figure out the cost now that you know what your package qualifies as --
https://postcalc.usps.com/ To see all possible options, choose "Calculate price based on Shape and Size" at the end of the first screen. When the actual list of prices appears, scroll down to see the first class options.
Yes, as Earlene mentions, sometimes postal workers can and do interpret the rules differently than what is correct (I have a long story about that), but you can always ask to talk to the postmaster or file a dispute on the USPS website if you feel you have a strong case that you're right. But you need to know the rules first -- and the best place to get educated on the rules is the USPS website.