Thermal expansion, magnetostriction, and magnetization measurements under magnetic field and hydrostatic pressure were performed on a UAu2Si2 single crystal. They revealed a large anisotropy of magnetoelastic properties manifested by prominent length changes, leading to a collapse of the unit-cell volume accompanied by breaking the fourfold symmetry (similar to that in URu2Si2 in the hidden-order state) in the antiferromagnetic state as consequences of strong magnetoelastic coupling. The magnetostriction curves measured at higher temperatures confirm a bulk character of the 50K weak ferromagnetic phase. The large positive pressure change of the ordering temperature predicted from Ehrenfest relation contradicts the more than an order of magnitude smaller pressure dependence observed by the magnetization and specific heat measured under hydrostatic pressure. A comprehensive magnetic phase diagram of UAu2Si2 in magnetic field applied along the c axis is presented. The ground-state antiferromagnetic phase is suppressed by a field-induced metamagnetic transition that changes its character from second to first order at the tricritical point.