The problem is with mixed units. Width deals with pixel width (I think). ColumnWidth deals with character width (I think). So, for example, you are setting D4 width in characters to B4 width in pixels. I modified part of your code to illustrate the difference.

...

# find initial width of B4
$w1 = $sheet->Range("B4")->Width;
my $cw1 = $sheet->Range("B4")->{ColumnWidth};

# find new width of B4
$w2 = $sheet->Range("B4")->Width;
my $cw2 = $sheet->Range("B4")->{ColumnWidth};

# set column D to cell width found for cell F4
$sheet  -> Range("D4") -> {ColumnWidth} = $w2;

# find width of column D
$w3 = $sheet->Range("D4")->Width;
my $cw3 = $sheet->Range("D4")->{ColumnWidth};

# set column F to 60
$sheet  -> Range("F4") -> {ColumnWidth} = 60;

# find width of column F
$w4 = $sheet->Range("F4")->Width;
my $cw4 = $sheet->Range("F4")->{ColumnWidth};

print "B4 width 1<$w1> 2 <$w2> D4 width <$w3> F4 width <$w4>\n";
print "B4 colwidth 1<$cw1> 2 <$cw2> D4 colwidth <$cw3> F4 colwidth <$c
+w4>\n";
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Which gives the result:

B4    width 1<48>   2 <105>      D4 width <555>    F4 width <318.75>
B4 colwidth 1<8.43> 2 <19.29> D4 colwidth <105> F4 colwidth <60>
[download]