Consider the sequences:
seq1       CCCCC
seq2       CCCCD
seq3       CCCCE
seq4       CCCCF
seq5       DDDDG
seq6       DDDDH

The last position seems to be highly variable, and one
might believe that C through H are equally likely there.  In the
first 4 positions, C might be more likely than D, but it
is also conceivable that there is really only one ancestral instance
each of C and D in each position 1-4, and they are really about equally 
probable, with C perhaps having an edge.

Any sequence weighting scheme that makes C less than twice
as probable as D in the first 4 positions will make C through F less
probable than G and H in the last positions.  

My program finds that C gets 1.75 counts in the first 4 positions,
and D gets 1.1.  This is a ratio of 1.6:1, much less than
2:1.  On the other hand, C through H all get one count in the last 
position, so they are all equally probable.

Interestingly, in an earlier version of the documentation, I used a
similar example:
seq1       CCCCCCCC
seq2       CCCCDDDD
seq3       CCCCEEEE
seq4       CCCCFFFF
seq5       DDDDGGGG
seq6       DDDDHHHH

It turns out that in the new version of the program, this example
gives C:D a ration greater than 2:1 in the first 4 positions (2.57:1.18).
This is not what one initially expects.  The reason for this strange
answer is that these sequences have the unlikely feature that they
exhibit many more changes in the last four positions (20) than in the 
first four (4).  Thus the most likely interpretation is that the
first four sites undergo substitutions at a slower rate than the
other four, and in the model the only way to slow the rate is to
decrease the variability of the site, which is done here by making
C more probable.  The file "virtcts" shows the number of counts 
("virtual counts") caused by this aspect of the likelihood function.
In this case, the C's in the first 4 postions have .48 virtual counts.

Next consider:
seq1       DDCCCCCCCC
seq2       CCDDCCCCCC
seq3       CCCCDDCCCC
seq4       CCCCCCDDCC
seq5       CCCCCCCCDD
seq6       GGEEEEEEEE
seq7       EEGGEEEEEE
seq8       EEEEGGEEEE
seq9       EEEEEEGGEE
seq10      EEEEEEEEGG
Here we clearly have two separate families, and the 5 sequences
within each family are very closely related.  By symmetry, any
sequence weighting method must weight each sequence the same,
and will conclude that C is 4 times more common than D.  However,
since we know that the first 5 sequences are closely related, 
it is likely that the 4 C's are caused by inheritence, and
really not much more likely than D.  My program finds 1.38
counts (depending on initialization) for C, and 1 for D in each position.
Similarly for E and G.

If only half the data is given,
seq1       DDCCCCCCCC
seq2       CCDDCCCCCC
seq3       CCCCDDCCCC
seq4       CCCCCCDDCC
seq5       CCCCCCCCDD
it is no longer clear that these sequences are closely 
related.  The abundance of C may reflect a serious selective
pressure.  In this case the program finds 3.71 C's and 1 D in
each position.  These two examples show the importance of including
distantly related sequences in the data when they are available.