In the bulk, LaCoO_{3} (LCO) is a paramagnet, yet the low-temperature ferromagnetism (FM) is observed in tensile strained thin films, and its origin remains unresolved. Here, we quantitatively measured the distribution of atomic density and magnetization in LCO films by polarized neutron reflectometry (PNR) and found that the LCO layers near the heterointerfaces exhibit a reduced magnetization but an enhanced atomic density, whereas the film's interior (i.e., its film bulk) shows the opposite trend. We attribute the nonuniformity to the symmetry mismatch at the interface, which induces a structural distortion related to the ferroelasticity of LCO. This assertion is tested by systematic application of hydrostatic pressure during the PNR experiments. The magnetization can be controlled at a rate of -20.4% per GPa. These results provide unique insights into mechanisms driving FM in strained LCO films while offering a tantalizing observation that tunable deformation of the CoO_{6} octahedra in combination with the ferroelastic order parameter.