Equations of state (EOSs) for uniform nuclear matter including Λ and Σ − hyperons are constructed with the variational method starting from the bare baryon interactions to study the structure and composition of neutron stars (NSs). For the nucleon sector, the Argonne v18 two-nucleon potential and the Urbana IX three-nucleon potential are adopted. On the other hand, for the hyperon sector, central two-body potentials that reproduce the experimental data on hypernuclei are employed as the Λ-nucleon, Σ − -nucleon and ΛΛ interactions. Since there are no experimental data on the odd-state component of the ΛΛ interaction, we prepare four odd-state ΛΛ interaction models, and calculate four EOSs of hyperonic nuclear matter for those interactions using the cluster variational method. The obtained maximum mass of NSs increases as the odd-state ΛΛ interaction becomes more repulsive, although it is still smaller than the recently observed masses of heavy NSs. Moreover, the critical density of Σ − strongly depends on the odd-state ΛΛ interaction. A phenomenological three-baryon repulsive force is employed in our variational calculations to explain the observed data on heavy NSs.