Hardhat framework is a light weight php framework. It will work with or without a database (although a database is recommended), and is designed to be flexible yet simple to use.
Hardhat has a very small footprint, and only needed modules are loaded at any point in time.
Since it can run without a database, it is suitable even for small fairly static sites.
Why use a framework on a staic site?
Hardhat has a preferred approach to development, which includes MySQL, Smarty, and JQuery. But these elements are not required and can be easily replaced with other components if you prefer.
If you have a functioning webserver, you should be able to get a site deployed in very short order. Read the Install Instructions here.
Hardhat is based on a schema driven database model. What that means to you is that if you add a column to a database table, it is automatically available to the view. This is a very flexible arrangement that I'm sure you will come to love.
Hardhat's database access is a little different than what you find out there but I think it is especially well suited to common tasks you will encounter while developing websites.