© 2017 American Physical Society. We analyze entanglement and nonlocal properties of the convex set of symmetric N-qubit states which are diagonal in the Dicke basis. First, we demonstrate that within this set, semidefinite positivity of partial transposition (PPT) is necessary and sufficient for separability - which has also been reported recently by Yu [Phys. Rev. A 94, 060101(R) (2016)2469-992610.1103/PhysRevA.94.060101]. Furthermore, we show which states among the entangled diagonal symmetric are nonlocal under two-body Bell inequalities. The diagonal symmetric convex set contains a simple and extended family of states that violate the weak Peres conjecture, being PPT with respect to one partition but violating a Bell inequality in such partition. Our method opens directions to address entanglement and nonlocality on higher dimensional symmetric states, where presently very few results are available.