Copy Paste Values only( xlPasteValues )

If you are wanting to just copy the whole column, you can simplify the code a lot by doing something like this:

Sub CopyCol()

    Sheets("Sheet1").Columns(1).Copy

    Sheets("Sheet2").Columns(2).PasteSpecial xlPasteValues

End Sub

Or

Sub CopyCol()

    Sheets("Sheet1").Columns("A").Copy

    Sheets("Sheet2").Columns("B").PasteSpecial xlPasteValues

End Sub

Or if you want to keep the loop

Public Sub CopyrangeA()

    Dim firstrowDB As Long, lastrow As Long
    Dim arr1, arr2, i As Integer

    firstrowDB = 1
    arr1 = Array("BJ", "BK")
    arr2 = Array("A", "B")

    For i = LBound(arr1) To UBound(arr1)

        Sheets("Sheet1").Columns(arr1(i)).Copy

        Sheets("Sheet2").Columns(arr2(i)).PasteSpecial xlPasteValues

    Next
    Application.CutCopyMode = False

End Sub

since you only want values copied, you can pass the values of arr1 directly to arr2 and avoid copy/paste.

code inside the For loop, inside the With block, after lastrow calculation:

Sheets("SheetB").Range(arr2(i) & firstrowDB).Resize(lastrow).Value = .Range(arr1(i) & 1).Resize(lastrow).Value