What prevents any one branch from acquiring too much power?

The principle of SEPARATION OF POWERS, written into the US Constitution.

The "Separation of Powers" principle was an idea embedded into the plans for American government by our founding fathers, based on their reading of Enlightenment political theory.  The terminology "separation of powers" was introduced by Charles-Louis de Secondat, the Baron of Montesquieu.  (Usually he's referred to as just "Montesquieu.")  He wrote an important work of political theory called The Spirit of the Laws, published in 1748.

Within his treatment of how governments will function best, Montesquieu argued that executive, legislative, and judicial functions of government ought to be divided between parts of the government, so that no one person or division of the government can infringe on the overall rights of others in the government or of the members of the society overall.

answer-the island had airfields that the u.s. military needed.