The post office was correct @casey-86. They cannot charge you any difference directly. USPS has something called APV - Automated Package Verification.
The APV system scans packages en route, measures, weighs, takes photos. If it's found you underpaid postage, they will charge you for the difference.
When the label is purchased through eBay USPS charges you through eBay. It should come out of either your eBay funds or your backup funding source. Rate will be consistent with eBay rates for the difference between the 5 and 6 lb package.
Sometimes APV doesn't catch it in which case you won't see a charge.
Check out the new inefficient Seller Hub 'All Filters' panel to see how much eBay disrespects sellers' time (click).
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