Select all the columns, then, from the Menu Bar:

<Format> <Columns> <AutoFit>

Each column will be *individually* sized to display the widest entry in that
column.

Try selecting all the columns in the range and Format>Column>Autofit Selection.

Which is what the double-click should be doing...........fitting to selection,
not expanding one character larger as you state.

Gord Dibben  MS Excel MVP

I've read through this thread and I think you may be able to use this macro.
It lets you specify a "buffer factor" value (a number greater than 1) to
increase a column width by (for example, 1.1 will make a column 10% wider
than the AutoFit width) to create "extra" white space for the text UNLESS
the column width is already the buffer factor or more larger, in which case
that width is preserved. The buffer factor is specified in the Const
statement... I used 10% for my tests; but, perhaps, you can use 1.05 (5%
extra white space)... you will have to test to see what minimum buffer
factor you can get away with.

Sub SizeToFit()
 Dim R As Range
 Dim X As Long, z
 Dim ColWidth As Double
 Const Tolerance As Double = 1.1  '10% extra room
 Set R = Worksheets("Sheet1").UsedRange
 For X = R.Column To R.Columns.Count
   ColWidth = Columns(X).ColumnWidth
   If Worksheets("Sheet1").Cells(Rows.Count, X).End(xlUp).Row = 1 Then
     If Worksheets("Sheet1").Cells(Rows.Count, X).Value = "" Then
       GoTo Continue
     End If
   End If
   Columns(X).AutoFit
   If Tolerance * Columns(X).ColumnWidth < ColWidth Then
     Columns(X).ColumnWidth = ColWidth
   Else
     Columns(X).ColumnWidth = Tolerance * Columns(X).ColumnWidth
   End If
Continue:
 Next
End Sub

Rick