Hybrid structures consisting of two-dimensional (2D) magnets and semiconductors have exhibited extensive functionalities in spintronics and opto-spintronics. In this work, we have fabricated WSe$_2$/Fe$_3$GeTe$_2$ van der Waals (vdW) heterostructures and investigated the proximity effects on 2D magnetism. Through reflective magnetic circular dichroism (RMCD), we have observed a temperature-dependent modulation of magnetic order in the heterostructure. For temperatures above $40$ K, WSe$_2$-covered Fe$_3$GeTe$_2$ exhibits a larger coercive field than that observed in bare Fe$_3$GeTe$_2$, accompanied by a noticeable enhancement of the Curie temperature by $21$ K. This strengthening suggests an increase in magnetic anisotropy in the interfacial Fe$_3$GeTe$_2$ layer, which can be attributed to the spin-orbit coupling (SOC) proximity effect induced by the adjacent WSe$_2$ layers. However, at much lower temperatures ($T<20$ K), a non-monotonic modification of the coercive field is observed, showing both reduction and enhancement, which depends on the thickness of the WSe$_2$ and Fe$_3$GeTe$_2$ layers. Moreover, an unconventional two-step magnetization process emerges in the heterostructure, indicating the short-range nature of SOC proximity effects. Our findings revealing proximity effects on 2D magnetism may shed light on the design of future spintronic and memory devices based on 2D magnetic heterostructures.
