There are lightweight alternatives to commonly-used libraries. Some do away with compatibility with old browsers, some are less bloated, and some just do less.
First and foremost, try customizing Bootstrap, rather than including all modules even if you aren't using them.
Otherwise, you can try these alternatives:
- Concise CSS
- Picnic CSS
- Tent CSS
Lightweight front-end frameworks
- Revised font stack, a list of typefaces that are preinstalled on most computers.
- Icomoon app allows you to select the icons you want and bundle them up to a minimal font or SVG.