How are you getting those numbers?Being loaded with nutrients, I still limit them as treats since eggs are 34% protein but a whopping 64% fat.
https://fdc.nal.usda.gov/fdc-app.html#/food-details/171287/nutrients
According to this, I see that 100g of whole raw egg has 76.2 g of water, 12.6 g of protein, and 9.51 g of fat.
Since it's working from 100 grams, the percents are easy:
76% water, 12.6% protein, 9.5% fat
Even if you are counting dry weight, ignoring the water, it still has more protein BY WEIGHT than fat (backwards of what you said.)