Not sure if I understand the question correctly but you seem to loop through the command line arguments. However, each time you read a file based on an argument you overwrite the old content of the textbox.
So perhaps you should have
Textbox.Text = Textbox.Text & zReader.ReadToEnd
Another thing is that you seem start looping the array from index 1. Should the starting position be 0?
EDIT:
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Based on the discussion the code should probably be something like
Shared Sub DoubleClickFile(Textbox As TextBox)
If System.Environment.GetCommandLineArgs().Length > 1 Then
Dim i As Integer
For i = 1 To System.Environment.GetCommandLineArgs().Length - 1
Dim zReader As StreamReader
zReader = New StreamReader(System.Environment.GetCommandLineArgs(i), True)
Textbox.Text = zReader.ReadToEnd
EditorForm.DocumentName = System.Environment.GetCommandLineArgs(i)
Next
End If
End Sub