Household Expenses are an abstracted representation of the living and luxury costs for the people in your household.
They start off low for babies and then rise linearly as they get older, and they also increase linearly as you get wealthier and move up social classes to represent the rising consumption in luxury, slaves, etc.
This also works as a gameplay balancing feature, in a way mimicking real life considerations that prevent a meteoric rise to riches.
You can see the current expenses on the Property Screen.
If things feel overwhelming, I would recommend that you get comfortable with the game on Easy Mode where things are not as taxing