Weight is perceived through the combination of multiple sensory systems, and a wide range of factors – including touch, visual, and force senses – can influence the perception of heaviness. There have been remarkable advancements in the development of haptic interfaces throughout the years. However, a number of challenges limit the progression to enable humans to sense the weight in virtual reality (VR). This article presents an overview of the factors that influence how weight is perceived and the phenomenon that contributes to various types of weight illusions. A systematic review has been undertaken to assess the development of weight perception in VR, underlying haptic technology that renders the mass of a virtual object, and the creation of weight perception through pseudo-haptic. We summarize the approaches from the perspective of haptic and pseudo-haptic cues that exhibit the sense of weight such as force, skin deformation, vibration, inertia, control–display ratio, velocity, body gestures, and audio–visual representation. The design challenges are underlined, and research gaps are discussed, including accuracy and precision, weight discrimination, heavyweight rendering, and absolute weight simulation. This article is anticipated to aid in the development of more realistic weight perception in VR and stimulated new research interest in this topic.