The maximum required thickness of lines in WebGL1 is 1 so basically your browser or OS or driver has a limit of 1 for line thickness.
In WebGL2 it's even more common for the limit to be 1 because it's 1 in OpenGL 4.0+ Core Profile.
From the OpenGL 4.+ specs, section E.2.1
E.2.1 Deprecated But Still Supported Features
The following features are deprecated, but still present in the core profile. They may be removed from a future version of OpenGL, and are removed in a forward compatible context implementing the core profile.
- Wide lines - LineWidth values greater than 1.0 will generate an INVALID_VALUE error.
While WebGL2 is based on OpenGL ES 3.0 on desktops it runs on top of OpenGL 4 or ANGLE both of which have a limit of 1. Since Firefox 51 and Chrome 56 shipped yesterday and both are using ANGLE or OpenGL 4+ on desktops that means the limit is now 1 pretty much everywhere even in WebGL1
The point of all of that is unless you only care about lines of with 1 you shouldn't use GL's line drawing to draw lines (yea, I know, sounds silly).
Instead you need to come up with some other solution.
Some links,
First a library for three.js
https://github.com/spite/THREE.MeshLine
Otherwise some articles about how to create lines
http://labs.hyperandroid.com/efficient-webgl-stroking
https://cesiumjs.org/2013/04/22/Robust-Polyline-Rendering-with-WebGL/
https://mattdesl.svbtle.com/drawing-lines-is-hard