I don't think WebAssembly will become more common than JavaScript anytime soon. And even when it will be, it means the tooling will have become so good that you won't even have to think about WebAssembly. That will be left to the people who create compilers to WebAssembly.
Hopefully you'll just use whatever language your org/team/etc. uses, and have it compiled to JS or WebAssembly as is most appropriate for said language.
To answer your other question, I most certainly hope we won't see "more Web stuff" built with C++. C++ is a terrible language for that. It's a very good language to do stuff that needs predictable high performance such as games. And games is a good market for C++ in the browser through WebAssembly. But other than that I hope other, more high level languages will pick up.
Hopefully you'll just use whatever language your org/team/etc. uses, and have it compiled to JS or WebAssembly as is most appropriate for said language.
To answer your other question, I most certainly hope we won't see "more Web stuff" built with C++. C++ is a terrible language for that. It's a very good language to do stuff that needs predictable high performance such as games. And games is a good market for C++ in the browser through WebAssembly. But other than that I hope other, more high level languages will pick up.