SNR and Voxel Size
Refer to these equations: SNR calculation and voxel size calculation. You can increase the voxel size by ↑ FOV, ↓ Ny, or ↑ slice thickness. The SNR is increased because there is more signal in each voxel. But isn't there more noise too? The noise is "white" (covering a wide range of frequencies, uncorrelated from measurement to measurement). This means the noise doesn't increase and so the signal-to-noise ratio goes up.
Tradeoffs: more partial volume artefact, decreases in-plane spatial resolution.
Further reading on this topic:
Books: MRI From Picture to Proton p73-74, 168, MRI The Basics p99
Online: MRItutor 1, 2