Having more people in your settlement can make future projects much easier to finish in Manor Lords, but you have to foster a strong community to increase its population. Keeping the families in your town safe will attract others to move in if you have the space. With a larger population, you can generate more revenue and invest in important expansions of your land that will let your city grow.
The city building of Manor Lords is incredibly detailed, with small parts of the game having a much larger impact on other aspects of your village than you might expect. For example, some resources can only be collected during one season of a long year. Failure to keep up with the limitations of the world due to time could severely decrease the chances of your community's survival before it can ever grow.

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How To Grow Total Population
Raise Your Approval For Your Community
The most consistent way to grow your population in Manor Lords is to raise the Approval Rating of your settlement to at least 50% as you organize your resources. Whenever your Approval is above this percentage, a new family will move into your village at the end of every month. This slow but steady increase can become even higher if you manage to raise Approval further.
Your Approval Rating also affects the Morale of the Militia raised from your settlement, making the statistic important for both population growth and military might.
One of the features of Manor Lords prevents you from accommodating new families if you do not have a Burgage Plot set aside as a place for them to live. Converting an empty plot into a space for new families is required regardless of your Approval Rating. As you start welcoming more people, you have to keep your Approval high by providing food and fuel to keep those living in your settlement fed and warm.
Other factors, such as Hunger, Church Level, Clothing Market Supply, and Marketplace Food Variety also impact total Approval. Should your Approval drop below 25%, families will start moving out of your community permanently. This medieval realism to classic RTS gameplay reflects how a village can grow distrustful of your leadership and quickly reduce the manpower you may need to operate important locations in your town.
The best advice for keeping Approval is to not raise taxes too high and to keep people alive through illness and other unfortunate situations. Even as you increase your population in Manor Lords, you only need to keep Approval above the minimum value to retain the people in your community who have chosen to stay.