plotting - Error bar plot - no bars but rather point size determined by errors

Looking for a way to create an ErrorListPlot (x,y,error) with the radius of the PlotMarker determined by the magnitude of the error (which in my case is symmetrical), no actual error bars desired.

I want the size of the points to reflect the standard deviation of the datum, rather than Small,Largeor anyAbsolutePointSize` values.

I can probably approach this a variety of ways (BubbleChart, ListPlot with custom PlotMarkers, or ErrorListPlot with custom ErrorBarFunction) but I can't make progress. All of my efforts are being foiled by the relative scaling of PlotMarkers to the width of the plot, rather than the magnitude of the data values.