Why are capital C, H, P, and Q bold in Unicode Double Struck Font?

I'm not sure what you mean. Unicode doesn't have fonts. It has code blocks and code points. Fonts are how your computer chooses to render those code points.

On my browser, I don't see anything special about C, H, P, or Q on the page that you link to. They look similar to all of the other double-struck characters. Perhaps the font you are using is wonky?

However, I did find this note on stackexchange:

https://stackoverflow.com/questions/28012644/whatever-happen...

It says that the mathematical blackboard-bold symbols appeared in Unicode first, and the full set of double-struck characters appeared later. That includes C (complex), H (quaternions), etc. It's possible that your font is rendering those as actual-bold (for which blackboard-bold was supposed to be a hand-written substitute).