@scanny the difference in the XML is

<w:tcW w:w="0" w:type="auto"/> compared to  <w:tcW w:w="1377" w:type="dxa"/>

@SebastienGutierrez is absolutely right, I created a small script to create a .docx-file demonstrating the problem for tables with and without autofit.

Whitespaces contribute to the problem and have to be included in test cases when trying to fix the problem.
The expected autofit-behaviour is achieved by replacing type="dxa"'with 'type="auto" in word/document.xml
table.autofit =False allways works as expected

Obviously this is not a proper solution, since there are several other occurences of 'dxa' in the code, thus replacing might destroy files other than my very simple test case (I have tried some other files without any problems).
I think CT_tbl._tcs_xml() in table.py has to be adjusted, but I just couldn't figure out how all the classes work together.

from docx import Document
from zipfile import ZipFile

document_file = 'AutofitTest.docx'
fixed_document_file = 'AutofitTest_fixed.docx'

doc = Document()

for autofit in [True, False]:
   doc.add_heading('Table with autofit = ' + str(autofit), 1)
   for text in ['NoWhiteSpaces', ' whitespaces ']:
       doc.add_heading('Test table: ' + text, 2)
       table = doc.add_table(2,2)
       table.autofit = autofit
       for row in table.rows:
           for cell, cell_text in zip(row.cells, ['A', 5 * text]):
               cell.text = cell_text
       doc.add_paragraph()
doc.save(document_file)

# Replacing type="dxa"'with 'type="auto" in word/document.xml 

with ZipFile(document_file, 'r') as myzip:
   with ZipFile(fixed_document_file, 'w') as myzip_out:
       for f in myzip.namelist():
           data = myzip.read(f)
           if f == 'word/document.xml':
               data = data.replace(b'type="dxa"', b'type="auto"')
           myzip_out.writestr(f, data)

autofit is broken #209

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