A combination of PointSize and LegendMarkerSize appear to be necessary to overcome the problem mentioned by @rcollyer in comments, i.e. the fact that, since the marker is a textual form with a font-size, there is an effective upper limit to the marker size.
Here is a helper function that takes a plot with a PointLegend and replaces the appropriate values within the plot with new user-defined ones to enlarge the legend markers:
ClearAll[enlargeLegendMarker]
enlargeLegendMarker[plotobject_, newsize_] :=
ReplaceAll[
plotobject,
Legended[plot_,
Placed[
legend_,
options__]
] :>
Legended[plot,
Placed[
Append[legend /. PointSize[_] -> PointSize[newsize], LegendMarkerSize -> 350 newsize],
options
]
]
]
The function takes a plot and a new fractional marker size as arguments. Note that an appropriate LegendMarkerSize must be calculated depending on the PointSize to have enough room for each marker at size. This was done by trial and error. A value of $350\times$ the new fractional size seems to work well.
Some definitions:
xy = {{1, 1}, {5, 7}, {10, 31}};
plot = ListLogLogPlot[{xy, 2 xy}, PlotLegends -> {"hey", "you"}];
And some usage examples:
{Style[#, 20], enlargeLegendMarker[plot, #]} & /@ {0.02, 0.05, 0.1, 0.3} // TableForm
