Thank you. It worked. I used /usr/libexec/weston-keyboard, because /usr/lib/weston/weston-keyboard did not exist. I think the actual solution was placing the weston.ini in ~/.config/weston.ini also (previously, it was located only in /etc/xdg/weston).
Now my problem is that the virtual keyboard is not displayed when accessing a text input box in GTK, due to the fact that Weston implements the interfaces for zwp_text_input_manager_v1, while gtk only supports zwp_text_input_manager_v3 (see link). However, if I use weston-editor, the virtual keyboard is displayed. Anyway, this is another problem (I will try Xorg/X11; hopefully, this problem will be gone).