A strong correlation between magnetic interaction and topological symmetries leads to unconventional magneto-transport behavior. Weyl fermions induce topologically protected spinmomentum locking, which is closely related to spin-wave gap formation in magnetic crystals. Ferromagnetic SrRuO3, regarded as a strong candidate for Weyl semimetal, inherently possesses a nonzero spin-wave gap owing to its strong magnetic anisotropy. In this paper, we propose a method to control the spin-wave dynamics by nanolayer designing of the SrRuO3/SrTiO3 superlattices. In particular, the six-unit-cell-thick SrRuO3 layers within the superlattices undergo a phase transition in crystalline symmetry from orthorhombic to tetragonal, as the thickness of the SrTiO3 layers is modulated with atomic-scale precision. Consequently, the magnetic anisotropy, anomalous Hall conductivity, and spin-wave gap could be systematically manipulated. Such customization of magnetic anisotropy via nanoscale heterostructuring offers a novel control knob to tailor the magnon excitation energy for future spintronic applications, including magnon waveguides and filters. Our nanolayer approach unveils the important correlation between the tunable lattice degrees of freedom and spin dynamics in topologically non-trivial magnetic materials.