Remove empty row after loop when moving to next worksheet while copying - excel

Question

I am trying to combine several worksheets into one more pivot-friendly layout.
I copy/paste from the existing worksheets into a new worksheet and rearrange the data. This works fine, but when the loop moves on to the next worksheet it adds an empty row below the data.
I know that this is a minor inconvenience but i want to wrangle the data as little as possible before turning it into a pivot table.
My code so far:
Sub NewPivot()
Dim iRow As Long, iWorksheetIndex As Long, iNumberOfWorksheets As Long, iRowCounter As Long, iCol As Long, lastCol As Long
Dim wbkSource As Workbook
Dim wksSource As Worksheet
Dim wbkTarget As Workbook
Dim wksTarget As Worksheet
Dim strActiveWorkbook As String
Workbooks.Open ("C:\\Source.xlsm")
Set wbkSource = Workbooks("Sheets.xlsm")
iWorksheetIndex = 1
Set wksSource = wbkSource.Worksheets(iWorksheetIndex)
strActiveWorkbook = ThisWorkbook.Name
Set wbkTarget = Workbooks(strActiveWorkbook)
Set wksTarget = wbkTarget.Worksheets(1)
iNumberOfWorksheets = wbkSource.Application.Sheets.Count 'Count number of worksheets
iRowCounter = 0
For iWorksheetIndex = 1 To iNumberOfWorksheets
lastCol = wbkSource.Worksheets(iWorksheetIndex).Cells(1, 1).End(xlToRight).Column
For iCol = 0 To lastCol - 2 'last Column
For iRow = 2 To 5
If wbkSource.Worksheets(iWorksheetIndex).Cells(1, 2 + iCol) <> "Sum" Then 'don't copy if the header of the data is a sum
'Copy data 01
wbkSource.Worksheets(iWorksheetIndex).Cells(iRow, 2 + iCol).Copy
wksTarget.Cells(iWorksheetIndex + iRowCounter, 1).PasteSpecial Paste:=xlPasteValues
'Copy data 02
wbkSource.Worksheets(iWorksheetIndex).Cells(1, 2 + iCol).Copy
wksTarget.Cells(iWorksheetIndex + iRowCounter, 2).PasteSpecial Paste:=xlPasteValues
'Copy data 03
wbkSource.Worksheets(iWorksheetIndex).Cells(iRow, 1).Copy
wksTarget.Cells(iWorksheetIndex + iRowCounter, 3).PasteSpecial Paste:=xlPasteValues
Else
Exit For
End If
iRowCounter = iRowCounter + 1
Next iRow
Next iCol
Next iWorksheetIndex
End Sub
EDIT: Spreadsheet layout:
Worksheet 1
Header1 | Header2
Data | Data
Data | Data
Data | Data
Worksheet 2
Header1 | Header2 | Header2
Data | Data | Data
Data | Data | Data
Data | Data | Data
Basically all worksheets contain a header and have varying numbers of columns but the same amount of rows (5)