The achievable precision in micro-machining is constrained by a phenomenon known as the size effect. The edge radius of the tool significantly influences the size effect leading to non-proportional scaling of process performance. The process becomes unscalable below a certain ratio of uncut chip thickness to edge radius termed as critical relative tool sharpness (RTS). Despite extensive studies on the size effect associated with non-linear process performance, very limited studies have focused on the critical RTS range. In the present study, orthogonal cutting experiments were conducted on a commercial aluminium alloy (Al6060) with different cutting-edge radiuses in the RTS range of 0.5 to 0.01. Extensive analysis of the morphology of the chips and tool-work material adherence has been carried out and correlated with the observed size effect on surface integrity. One of the key findings in this study was the size effect in the chips with respect to the chip curl radius and pitch. Between RTS 0.5 and 0.09, an increase in chip curl and pitch is observed, followed by a sharp fall up to RTS 0.07. In addition, another notable phenomenon was the formation of dual-layered chips with deformed layer on the rake side and lamellae like features on the free side. Furthermore, size effect was observed in surface roughness, surface hardness and flank adherence. In summary, the present investigation offers a comprehensive understanding of the size effect within the critical RTS range elucidating its multifaceted impact on micro-cutting.