Babies start reaching to be picked up around 4-6 months of age. This milestone is a significant indicator of motor and cognitive development. As babies reach this stage, they develop the ability to coordinate their arm and hand movements, allowing them to extend their arms towards a desired object or person for interaction or comfort. This behavior is influenced by their growing awareness of self and their surroundings, and it serves as a means of communication and emotional bonding with their caregivers.