What does it offer to an object oriented language such as C++? or is it not possible to use GTK+ without it?
Is the GObject implementation of objects is of a similar quality to that of C++ in terms of the size and speed of an executable assuming both examples use the same compiler? Or are there some trade-offs where GObject would be slower on the account of additional capabilities it provides?
GObject (a bit like COM in the Windows world) is a C API designed with cross language interoperability in mind.
This means that you can use GObjects in any language which supports calling C functions, but this makes it very difficult to write GObjects in a non-C language which are truly reusable from any language (if you write a GObject derived class in say, Python, you'd have to embed a Python interpreter every time you wanted to use objects from this class in C).
It is possible to semi-automate the creation of bindings for many languages (eg. Python, Perl, JS etc), and here lies one of the strengths of GObject. This accounts for the somewhat opaque API that GObject provides, which is, I confess, quite difficult to understand thoroughly.
Unfortunately, it doesn't fit well within the C++ language either. GObjects have no trivial relationship with C++ classes, and even if bindings are available (Gtkmm) it is not possible to easily write a C++ class "inheriting from GObject" and expose it to the world. You have to write C for this.
[What the world would need would be some kind of extensions to the C++ language which would make it easy to interop with GObject, a little like C++Cx on Windows, but 1) it is a difficult task, perhaps achievable through a GCC plugin, and 2) there is no momentum towards C++ in the Gnome world, or generally in the Linux world (KDE being a notable exception). For now we are stuck with the Gtkmm bindings.]