It depends what you mean by "heavy", but the common example is something like thread-per-request or implementing async IO using threads that make blocking calls.

In those context threads are primary "heavy" because each thread needs a dedicated stack, so there is a pretty low limit on the total number of threads you can have based on your available memory, so you run into scaling limitations whenever you'd naturally want to have 100 of thousands or millions of such threads.

The CPU use of context switches is a secondary factor there and probably pales compared to IO costs - and some competing designs also have context switch costs.

Threads were also heavy in the sense that if they are OS scheduled, the behavior often degrades with large numbers of threads, depending on the implementation. Recent scheduler designs are mostly able to mitigate this, however.