We present the first ALMA dust polarization observations toward the high-mass star-forming regions W51 e2, e8, and W51 North in Band 6 (230 GHz) with a resolution of about (∼ 5 mpc). Polarized emission in all three sources is clearly detected and resolved. Measured relative polarization levels are between 0.1% and 10%. While the absolute polarization shows complicated structures, the relative polarization displays the typical anticorrelation with Stokes I, although with a large scatter. Inferred magnetic (B) field morphologies are organized and connected. Detailed substructures are resolved, revealing new features such as comet-shaped B-field morphologies in satellite cores, symmetrically converging B-field zones, and possibly streamlined morphologies. The local B-field dispersion shows some anticorrelation with the relative polarization. Moreover, the lowest polarization percentages together with largest dispersions coincide with B-field convergence zones. We put forward , where ω is the measurable angle between a local B-field orientation and local gravity, as a measure of how effectively the B field can oppose gravity. Maps of for all three sources show organized structures that suggest a locally varying role of the B field, with some regions where gravity can largely act unaffectedly, possibly in a network of narrow magnetic channels, and other regions where the B field can work maximally against gravity.