Shipping Help

I have a store with various weights and products. For shipping in the US, I want to use USPS Priority boxes for most everything. The problem is how to set up shipping or find an extension to do the job. The customer should not have an option of what costs to select for shipping, but instead it should be calculated based on weight, size or amount of items ordered. Doesn't matter which method I use as long as it is accurate.

Here is a basic run down of what could be ordered in the shop:
1 1/8 ounce bottle of aromatherapy oil or up to 30 1/8 ounce bottles,
one blanket 11oz needing a large box
and someone could order multiples of these or mix and match products
There are other sizes and instances like this in the store. Weights are not a lot, but for instance the bottles need to be protected in a box as well as a few other products being sold.

I have looked around on the forums, looked for extensions and played with options in OC. No luck so far.

Found one item that was still installed. Removed and works fine