If an order qualifies for multiple shipping rules, the rule(s) for the most specific destination would override any other rule(s) for broader destinations -- e.g., a rule for Country:US would override a rule for Country:all, and a rule for Country:US and State:AZ would override a rule for Country:US and State:all.
It appears you created all of your new country-specific rules with Max. Weight = 8.00, so they only apply to orders with a total shipping weight up to 8 oz.; if an order's total shipping weight is above 8 oz., those rules would not apply, thereby allowing your Country:all rule(s) to apply instead.
It looks like you'd set up your other rules for Country:all and Country:US like so:
- One flat rate per order up to Max. Weight = 499 oz.;
- A different flat rate for single items of Min. Weight = 500 oz. and up;
- Another per-item rate for 2 or more items of Min. Weight = 500 oz. and up.
You'll probably want to match that scheme for your new country-specific rules. That 500 oz. breakpoint also appears to be a non-literal weight to handle DVD shipping rates differently from other items -- i.e., the single-item over 500 oz. rule would be the rate to ship a single DVD to the selected country, and the 2 or more items over 500 oz. rule would be the per-DVD rate to ship multiple DVDs to the selected country.
Finally, I noticed you have a Country:all rule for the USPS Cheapest rate, which I'm thinking may have been created in error; if so, just select Rule#125166 in the Existing Shipping Rules menu and Delete that.