ABSTRACT Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering σ8 and matter density parameter Ωm. The main nuisance parameter in a cluster weak lensing cosmological analysis is the scatter between the true halo mass and the relevant cluster observable, denoted $\sigma _{\ln M_\mathrm{ c}}$. We show that combining the cluster weak lensing observable ΔΣ with the projected cluster–galaxy cross-correlation function wp,cg and galaxy autocorrelation function wp,gg can break the degeneracy between σ8 and $\sigma _{\ln M_\mathrm{ c}}$ to achieve tight, percent-level constraints on σ8. Using a grid of cosmological N-body simulations, we compute derivatives of ΔΣ, wp,cg, and wp,gg with respect to σ8, Ωm, $\sigma _{\ln M_\mathrm{ c}}$, and halo occupation distribution (HOD) parameters describing the galaxy population. We also compute covariance matrices motivated by the properties of the Dark Energy Survey cluster and weak lensing survey and the BOSS CMASS galaxy redshift survey. For our fiducial scenario combining ΔΣ, wp,cg, and wp,gg measured over 0.3-30.0 h-1 Mpc, for clusters at z = 0.35-0.55 above a mass threshold Mc ≈ 2 × 1014 h-1 M⊙, we forecast a $1.4{{\ \rm per\ cent}}$ constraint on σ8 while marginalizing over $\sigma _{\ln M_\mathrm{ c}}$ and all HOD parameters. Reducing the mass threshold to 1 × 1014 h 1 M⊙ and adding a z = 0.15-0.35 redshift bin sharpens this constraint to $0.8{{\ \rm per\ cent}}$. The small-scale (rp < 3.0 h-1 Mpc) ‘mass function’ and large-scale (rp > 3.0 h-1 Mpc) ‘halo-mass cross-correlation’ regimes of ΔΣ have comparable constraining power, allowing internal consistency tests from such an analysis.