First a technical point, the Marines are not a part of the Navy, they are a part of the Department of the Navy. It sounds like semantics, but theres technically a difference. The Navy is commanded by the Chief of Naval Operations. The Marines are commanded by the Commandant of the Marines. Both of these are the senior military commanders of each branch. These two people both report to the Secretary of the Navy, who is a CIVILIAN appointed by the President. The Marines do not directly report to the Navy, but only to the senior civilian oversight of the Department of the Navy.

To your actual point, during the British empire period, marines were the soldiers of the ship, used for ship to ship fighting and defense. Initially they were actually British soldiers transferred from the army and temporarily assigned to ships. Founded in 1664, The Duke of York and Albany’s Maritime Regiment of Foot, was created to support the Royal Navy, however it was still considered a regular army land unit of line infantry. When the later Royal Marines were created, they used the same structures of their predecessors, and then in 1775 when the US Marines were created, they copied their British counterparts. The rest is entirely from tradition.