Magnetic skyrmions are nanosized magnetization whirls that exhibit topological robustness and nontrivial magnetoelectrical properties, such as emergent electromagnetism and intriguing spin dynamics in the microwave-frequency region. In chiral magnets, skyrmions are usually found at a pocket in the phase diagram in the vicinity of the ordering temperature, wherein they order in the form of a hexagonal skyrmion lattice (SkL). It is generally believed that this equilibrium SkL phase is a uniform, long-range-ordered magnetic structure with a well-defined lattice constant. Here, using high-resolution small-angle resonant elastic x-ray scattering, we study the field and temperature dependence of the skyrmion lattice in FeGe and Cu₂OSeO₃ membranes. Indeed, Cu₂OSeO₃ shows the expected rigid skyrmion lattice, known from bulk samples, that is unaffected by tuning field and temperature within the phase pocket. In stark contrast, the lattice constant and skyrmion size in FeGe membranes undergo a continuous evolution within the skyrmion phase pocket, whereby the lattice constant changes by up to 15% and the magnetic scattering intensity varies significantly. Using micromagnetic modeling, it is found that for FeGe the competing energy terms contributing to the formation of the skyrmion lattice fully explain this breathing behavior. In contrast, for Cu₂OSeO₃ this stabilizing energy balance is less affected by the smaller field variation across the skyrmion pocket, leading to the observed rigid lattice structure.