"No Shipping Rates Found For This Address" - PLEASE HELP ASAP Losing Customers

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My store is pretty new. When I set it up I didnt have this issue. I tried to do a test of products in my store because everything was shipping priority at $8.35. I was loosing money. I adjusted the weights and verified my shipping rates. Upon testing several items, it appears that once the weight exceeds the weight for the priority shipping I get the error. For example I put 4 items in my cart that weighed 3lbs02.15ounces. The shipping showed only once choice pf priority at $8.35. I then added 4 more to the cart then I got the message. I tried another item. I put 10 coffee mugs in the cart and it showed only one shipping rate of priority of$8.35. Added 5 more, then I got the message.

I have another store that I tested. I do get more shipping rate options at checkout, but the Priority rates are very low. I have adjusted the weight of the items and for 15lbs its saying the shipping rate is $7.35. I need help.