Changing data series line weights in Excel chart (many at once)

Probably easiest to write a quick macro, somthing like

Sub SetWeights()
    Dim srs As Series
    For Each srs In ActiveSheet.ChartObjects("Chart 1").Chart.SeriesCollection
        srs.Format.Line.Weight = 0.75
    Next
End Sub

This is a more copy-and-paste compatible version of Chris's answer:

Sub SetWeights()
    Dim srs As Series
    For Each srs In ActiveChart.SeriesCollection
        srs.Format.Line.Weight = 0.25
    Next
End Sub

Just select the chart and run the macro.

Enhancement: create a VB variable (LineWT) that points to a cell in the spreadsheet. Then instead of "Format.Line.Weight = 0.25" change 0.25 to LineWT. Then you can change the line weight by changing it on spreadsheet and clicking the macro button. You can use similar code to set X/Y Axes names with pointers to the spreadsheet.