A heavier fill will provide a warmer bag compared to a similarly constructed bag of equivalent fill.

The accuracy of any rating of sleeping bag depends upon the rating methodology used by the manufacturer. Some like to lie more than others. Slumberjack. They greatly inflate the temperature rating and deflate the weight by several ounces.

A down bag of only 8 ounce fill with 800 cu.in./oz will be warmer than a synthetic bag of only 8 ounce fill and it will be warmer than a down bag of only 8 ounce fill of lower quality down, say 600 cu.in./oz. Weight, alone, isn't a measure of warmth or accuracy of the methodology used by the manufacturer.

There is some value to the weight and warmth relationship, but less as an absolute. In the interest of quick communication, you may have oversimplified.