I've created a simple sample application with 5000 concurrent goroutines, tuned to have around 30 % CPU usage (on my desktop PC) without profiling. After profiling was enabled with 5 % sample rate, the CPU usage jumps to around 40 %.

I've run a pprof CPU profile with and without profiling enabled. In the following SVG, you can see that the vast majority of the overhead is coming from calling Runtime.stack(). Current profiling implementation calls it periodically to collect stacks for all goroutines. Therefore, the time complexity increases with the number of active goroutines.
See the profile output as a tree (.svg so you can zoom in)

I'm investigating how we could improve this.

Note: runtime.GoroutineProfile() has lower overhead, possibly because it doesn't produce string output, but it currently doesn't have a goroutine ID so we can't map stacks across multiple calls to a single routine, see golang/go#59663