Carb intake the night before (evening meal and/or snacks) has never made much difference to my DP. I often have minimal, or no carb evening meals (just some meat and green beans, or steak and salad), yet my DP has always chugged away. Something different happens with the longer fasting. And long may it continue.
For me, as a particularly insulin resistant individual, I think it gets a lot more complicated than carbs. Protein and nucleogenesis, glycogen storage, insulin resistance through background insulin, cortisol, growth hormone, and all the other balancing hormones... they play a part.
But not everyone has this. Sometimes just cutting carbs is enough to make the weight fall off and insulin resistance/DP to normalise.