We investigate spin correlations in the dipolar Heisenberg antiferromagnet Gd2Sn2O7 using polarised neutron-scattering measurements in the correlated paramagnetic regime. Using Monte Carlo methods, we show that our data are sensitive to weak further-neighbour exchange interactions of magnitude ∼0.5% of the nearest-neighbour interaction, and are compatible with either antiferromagnetic next-nearest-neighbour interactions, or ferromagnetic third-neighbour interactions that connect spins across hexagonal loops. Calculations of the magnetic scattering intensity reveal rods of diffuse scattering along [1 1 1] reciprocal-space directions, which we explain in terms of strong antiferromagnetic correlations parallel to the set of [Formula: see text] directions that connect a given spin with its nearest neighbours. Finally, we demonstrate that the spin correlations in Gd2Sn2O7 are highly anisotropic, and correlations parallel to third-neighbour separations are particularly sensitive to critical fluctuations associated with incipient long-range order.