Even if I only use one or two features of a large library, by linking to that library am I going to incur runtime performance overheads?
In general, no.
If the library in question doesn’t have a lot of position-independent code, then there will be a start-up cost while the dynamic linker performs relocations on the library when it’s requested. Usually, that’s part of the program’s start-up. There is no run-time performance effect beyond that.
Linkers are also good at removing “dead code” from statically-linked libraries at build time, so any static libraries you use will have minimal size overhead. Performance doesn’t even enter into it.
Frankly, you’re worrying about the wrong things.