Magnetic materials with competing magnetocrystalline anisotropy and dipolar energies can develop a wide range of domain patterns, including classical stripe domains, domain branching, and topologically trivial and nontrivial (skyrmionic) bubbles. We image the magnetic domain pattern of Fe3Sn2 by magnetic force microscopy and study its evolution due to geometrical confinement, magnetic fields, and their combination. In Fe3Sn2 lamellae thinner than 3 μm, we observe stripe domains whose size scales with the square root of the lamella thickness, exhibiting classical Kittel scaling. Magnetic fields turn these stripes into a highly disordered bubble lattice. Complementary micromagnetic simulations quantitatively capture the magnetic field and thickness dependence of the magnetic patterns, reveal strong reconstructions of the patterns between the surface and the core of the lamellae, and identify the observed bubbles as skyrmionic bubbles. Our results imply that geometrical confinement together with competing magnetic interactions can provide a path to fine-tune and stabilize different types of topologically trivial and nontrivial spin structures in centrosymmetric magnets.