The principles identified in the Declaration were based on natural law. People are subject to the laws of nature. The Constitution was wrutten by men who considered it to be a self evident truth that all men were created equal and were endowed by their Creator with certain unalienable rights.
When they wrote the Constitution they wanted it to create government that would be aligned with the principles expressed in the Declaration of Independence. They understood that with liberty comes responsibility.
The states wanted their new government to provide for their common defense, establish justice, insure domestic tranquility, and promote the general welfare. In order to constrain the government from abusing the power. They delegated to the governemnt a short list of enumerated powers. The powers not delegated to the government of the united States, nor prohited to the states were reserved to the states and the people.
The founders wanted to create a more perfect union, not an all powerful central government.