We analyze the ground-state properties of three-body constrained bosons in a one-dimensional optical lattice with staggered hoppings analogous to the double-well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint, several gapped phases such as the Mott insulators and dimer–bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair–bond-order phase at unit filling, which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities, we see the signatures of the gapless pair superfluid phase.