The last few days my store has been allowing customers to select First Class mail when the weight total far exceeds the upper limit for First Class. This has not happened before and I can't figure out why it is giving First Class as an option on the shipping page during check out.

Hi, have you taken a look at the weight showing in the admin for these orders?

Are you able to replicate this on your website?
Perhaps, if you cannot, try loading up the exact item(s) the customer did and use their same address, in a cart and see if you can replicate this.
If so, you might get a copy of the XML that is sent to shipping carriers by adding this parameter to your includes.php file...
$dumpshippingxml=TRUE;
...then run through a test transaction and you should get the XML displayed on the page. Then copy the XML and then take the parameter out again so customers are not seeing that.

You can message Vince, or me the XML output if you are unable to decipher the results.

Thanks,
David