the weighted reciprocal lattice
The bare reciprocal lattice tells you WHERE diffraction spots can appear, but not how bright each one is — every point looks the same. The weighted reciprocal lattice fixes that: it is the reciprocal lattice with a number attached to each point, a weight that says how strong the reflection at that point will be. Picture the plain reciprocal lattice as a blank street map and the weighted version as the same map with a brightness printed at every intersection. The weighted lattice is what a diffraction experiment actually shows you.
The weight on the point (hkl) is the diffracted intensity, which is proportional to the modulus-squared of the structure factor, written |F_hkl|^2. The structure factor F_hkl is the sum of the waves scattered by every atom in the motif, added up with their relative phases; it depends on WHAT atoms sit WHERE inside the unit cell. So the geometry of the reciprocal lattice (the positions of the points) comes from the lattice alone, while the weights come from the motif. This is the deep division of labour in diffraction: peak POSITIONS give you the unit cell, peak INTENSITIES (the weights) give you the contents. Some weights come out exactly zero — those are the systematic absences, whole rows or classes of reciprocal points switched off by lattice centering, screw axes, or glide planes, and their pattern of missing weights is a fingerprint of the space group.
This is why a diffraction pattern is more than a picture of the reciprocal lattice — it is a picture of the WEIGHTED reciprocal lattice, spots of differing brightness. It also frames the central difficulty of crystallography honestly: the experiment measures the weights (intensities, proportional to |F|^2) but loses the PHASE of each F. Without the phases you cannot run the inverse Fourier transform back to the atoms, and recovering them is the phase problem. So the weighted reciprocal lattice you can measure is genuine but incomplete — it holds the magnitudes and hides the phases.
In a body-centred cubic crystal, the structure factor makes F_hkl = 0 whenever h+k+l is odd. So on the weighted reciprocal lattice, the point (100) has weight zero (absent) while (110) has full weight (present). The lattice of possible points is complete; the weights knock out half of them.
Positions come from the lattice; brightnesses (and the zeros of systematic absences) come from the motif via the structure factor.
A zero weight (a systematic absence) does not mean the reciprocal point is missing from the lattice — the point is there, but the motif makes its structure factor cancel. Positions and weights answer two different questions.