Is a field created by a magnet also an excitation and does this field weight something? An excited electromagnetic field is a photon and an excited electric field is an electron. But if I have a magnet it creates a magnetic field but is this field also an excitation of a magnetic field. 
Does this magnetic field has a weight?
 A: According to our current understanding, there is no separate electric field or magnetic field. We treat them as one single entity called the electromagnetic field. In fact, these two fields were the first to be unified in physics.
QED, our current theory that explains these fields (awesomely), treats photons as excitations of this electromagnetic field. These photons are said to mediate the electromagnetic force.
The magnetic field you refer to in your example of say a bar magnet is also an electromagnetic field driven (in the case of bar magnets) by the spin angular momenta of the constituent particles of the magnet. It is only called a magnetic force for historical reasons. 
Now to your main question: Does this (electro)magnetic field have a weight?
Yes. Electromagnetic fields contain energy and all things that contain energy participate in gravitation interactions which is what we commonly interpret as weight. In case you meant mass then the answer would have been no. Photons are massless particles.
P.S.:- In your question you have said that electrons are excitations of the electric field. That assertion is incorrect. Electrons are excitations of the electron field (which is a very different entity than an electric field).
A: A magnet induces an electromagnetic field, whose excitations are photons, just the same as the electromagnetic field induced by an electron.
