Atomic weight is a measurement. Atomic matter is just that; the matter you are measuring with atomic weight.

Matter is anything with mass. The terms 'atomic weight' and 'atomic mass' are more or less interchangeable when speaking informally. Strictly speaking, one Dalton (formerly one Atomic Mass Unit or AMU) measures mass, not weight. The word substitution is highly ingrained in our language.

1) the term "atomic weight" is still used for historical reasons. The correct term is "atomic mass". Further information: http://www.answerbag.com/a_view/5127733 See also this reference if you wanted to know the difference between "atomic weight" and "atomic mass". 2) The term "atomic matter" could mean the quantity of matter inside an atom. This quantity is often measured with use of the mass number, which is the total number of protons and neutrons inside the atom. The reasons are: - compared to those of the proton and neutron, the mass of the electrons is much lower (9.11 × 10^−31 kg) - the mass of the neutrons (1,839 times the mass of electrons) and protons (1,836 times that of the electron) is very similar. "An atom has a mass *approximately* equal to the mass number times the atomic mass unit." Note the "approximately"! "Because the large majority of an atom's mass comes from the protons and neutrons, the total number of these particles in an atom is called the mass number. The mass of an atom at rest is often expressed using the unified atomic mass unit (u), which is also called a Dalton (Da). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately 1.66 × 10−^27 kg." Source and further information: http://en.wikipedia.org/wiki/Atom 3) The term "atomic matter" is also used in opposition to: - molecular matter: "At the surface of the Earth, atoms combine to form various compounds, including water, salt, silicates and oxides. Atoms can also combine to create materials that do not consist of discrete molecules, including crystals and liquid or solid metals. This atomic matter forms networked arrangements that lack the particular type of small-scale interrupted order associated with molecular matter." Source and further information: http://en.wikipedia.org/wiki/Atom - subatomic or QCD matter: "A subatomic particle is an elementary or composite particle smaller than an atom. Particle physics and nuclear physics are concerned with the study of these particles, their interactions, and non-atomic matter. Subatomic particles include the atomic constituents electrons, protons, and neutrons. Protons and neutrons are composite particles, consisting of quarks. A proton contains two up quarks and one down quark, while a neutron consists of one up quark and two down quarks; the quarks are held together in the nucleus by gluons. There are six different types of quark in all ('up', 'down', 'bottom', 'top', 'strange', and 'charm'), as well as other particles including photons and neutrinos which are produced copiously in the sun." Source and further information: http://en.wikipedia.org/wiki/Subatomic_particle "Quark matter or QCD matter (see QCD) refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons. These theoretical phases would occur at extremely high temperatures and densities, billions of times higher than can be produced in equilibrium in laboratories. Under such extreme conditions, the familiar structure of matter, with quarks arranged into nucleons and nucleons bound into nuclei and surrounded by electrons, is completely disrupted, and the quarks roam freely in what is called a quark gluon plasma. This is analogous to the way that the crystal structure of ice is disrupted by heating or compression, and melts into a liquid of more elementary constituents (water molecules)." Source and further information: http://en.wikipedia.org/wiki/QCD_matter