@Brett has just posted something along the lines of what I was thinking. I had a look at the code for the cell statistics and it uses CurrentValue
so a manual approach would be to evaluate:
Dynamic@CurrentValue[EvaluationNotebook[], "ByteCount"]
and then click on a cell bracket and observe the byte count. This can probably be automated using SelectionMove
to step through the cells and record the byte count.

Edit
Using SelectionMove
(I added a pause just to watch it working)
x = {};
Do[SelectionMove[nb, Previous, Cell];
x = {x, First@CurrentValue[EvaluationNotebook[], "ByteCount"]};
Pause[0.5], {15}];
Flatten[x]
(* {932, 7258, 992, 1039, 2150, 35190, 2121, 992, 2584, 9408, 1016, \
1791, 1529, 1657, 2775} *)
In principle you can also record the cell label and thereby identify which cell has large byte counts. For some reason this was not working for me and i haven't been able to figure out what the problem is. It works fine in the documentation notebook:

However when I cut and paste the code into a notebook and evaluate it doesn't work:

So if someone can explain why I am failing to obtain a cell label then the Do
loop above can be modified to record the cell label and corresponding byte count.
Edit #2
restarted Mma and now this is working, so starting from the bottom of your notebook (selecting 15 cells in this example):
x = {};
nb=EvaluationNotebook[];
Do[SelectionMove[nb, Previous, Cell];
x = {x, {Options[NotebookSelection[nb], CellLabel][[-1, 2]],
First@CurrentValue[nb, "ByteCount"]}};
Pause[0.5], {15}];
Partition[Flatten[x], 2]
(* {{"Out[122]=", 14811}, {"In[123]:=", 10149}, {"Out[93]=",
3490}, {"In[91]:=", 7127}, {None, 992}, {"Out[90]=",
1006}, {"In[90]:=", 2134}, {"Out[89]=", 35008}, {"In[89]:=",
2071}, {None, 992}, {"In[87]:=", 2543}, {"Out[86]=",
9259}, {"In[86]:=", 1015}, {"In[85]:=", 1785}, {"In[84]:=", 1515}} *)
or for a big notebook limit the output to byte counts above a certain level
Cases[Partition[Flatten[x], 2], {_, x_ /; x > 10000}]
(* {{"Out[122]=", 14811}, {"In[123]:=", 10149}, {"Out[89]=", 35008}} *)
Edit #3
In response to @Chris conversation
nb = EvaluationNotebook[];
Do[
SelectionMove[nb, Previous, Cell];
tmp = First@CurrentValue[nb, "ByteCount"];
If[tmp > 10000,
SetOptions[NotebookSelection[nb], CellDingbat -> "Big"]];,
{15}];