Try this version. Your code was setting up lots of nested loops but then ignoring that and just working on the selected table, over and over again.
Code:
Sub aaa()
Dim oSec As Section, oHead As HeaderFooter
Dim oTbl As Table, oCell As Cell
For Each oSec In ActiveDocument.Sections
For Each oHead In oSec.Headers
For Each oTbl In oHead.Range.Tables
With oTbl
'this would be the preferred method
.RightPadding = 0
.LeftPadding = 0
.TopPadding = 0
.BottomPadding = 0
.Spacing = 0
'and include 'same as table' for all cells
'But there isn't a method to make all cells 'same as table' other than with SendKeys
'... instead we will assign the same settings to every cell
For Each oCell In oTbl.Range.Cells
With oCell
.TopPadding = 0
.BottomPadding = 0
.LeftPadding = 0
.RightPadding = 0
End With
Next oCell
End With
Next oTbl
Next oHead
Next oSec
End Sub