Cross sections are a bathymetric sample of the river form over a particular reach. Depending on their location, they can approximate the channel form and transport capacity well, or poorly. A 1D model assumes the cross section is representative of the control volume. Small divergences between the measured cross section and the reach-average behavior do not usually trouble hydraulic simulations (unless cross section selection is egregious, like missing a control point or non-orthogonal placement). But small hydrodynamic differences between cross sections can causes local deposition and erosion in an equilibrium sediment transport model.

Transport capacity fluctuates from cross section to cross section due to random changes in transport capacity. Sediment scoured from one cross section is often deposited in the next cross section. This numerical artifact often generates oscillations, alternating erosion-deposition patterns, particularly early in a simulation. 

Cross Section Weights Editor (Press the Show XS Weights to show this).

HEC 6 introduced cross section weighting factors to smooth out these effects. Cross section weighting factors average the hydrodynamic parameters of several cross sections to compute transport capacity. Earlier versions of HEC-RAS adopted this feature as well as the 0.25-0.5-0.25 weighting default. This default gave half the weight to the computational cross section, and quarter weight to the upstream and downstream cross sections. The upstream and downstream weights could also be spread over multiple cross sections.

However, these weighting factors can also cause model instabilities (see Modeling Note). The defaults for this method changed in version 5.0, and more recent versions de-emphasized this feature even more, by requiring users to press a button to view this feature.
HEC-RAS retains hydraulic weighting for backward compatibility and user flexibility, but it is not recommended for most models, particularly simplified cross sections (e.g. trapezoid or rectangular channels). Current versions of HEC-RAS include "Warm Up" and hotstart options to deal with early simulation cross section adjustments.

Modeling Note: Saw Tooth Instability and Weighting Factors

A "Saw Tooth" instability often indicates errors propagated by cross section weighting factors. Weighting factors are particularly problematic with rectangular, trapezoidal, or other simple cross sections. Try setting weighting factors to 0-1-0, which will only use hydrodynamics from the current cross section for sediment capacity calculation.