What type of government has a powerful parliament and a weak king?

Constitutional monarchies divide power between the monarch (king or queen) and the parliament according to fixed rules laid out in the nation's constitution. As democratic political ideas have spread throughout the world, constitutions have, generally, been altered to allot more power to citizens (via a strong parliament) and less to the monarchy. Thus many modern constitutional monarchies are essentially democratic (or republican) in nature but retain the monarchy as a symbolic head of state for the sake of tradition. The United Kingdom, which is currently nominally governed by Queen Elizabeth II, is one example of this trend.
However, it is important to understand that "constitutional monarchy" does not necessarily mean a strong parliament and a weak monarch. Historically, constitutional monarchies often exhibited a power struggle between the parliament and the monarch, and the power of each branch ebbed and flowed.
https://www.royal.uk/role-monarchy