This looks good, but it can be simplified quite a bit. You can just store an integer on the entry with g_object_set_data and GPOINTER_TO_INT and GINT_TO_POINTER. Also g_object_get_data will return NULL if it doesn't find the data, so that'll be fine for the counter since GPOINTER_TO_INT(NULL) returns 0.
That also elimiates the need for the struct member in PidginConversation which we can't do because it breaks abi.

The imhtml is the widget that's being resized so you don't need to check it against anything else. So the check against entry shouldn't be necessary.
You should be able to get away with something like 
```c

gpointer raw_resize_count = NULL;

gint resize_count = 0;
raw_resize_count = g_object_get_data(G_OBJECT(imhtml), "resize-count");

resize_count = GPOINTER_TO_INT(raw_resize_count);
if(resize_count > MAX_RESIZE_COUNT) {

    return;

}
resize_count++;
g_object_set_data(G_OBJECT(imhtml), "resize-count", GINT_TO_POINTER(resize_count);

I'd have preferred if this could have been done on the PidginConversation instead of leaking into the GtkIMHtml, but it seems you can't get a signal in before the size-allocate object handler, so that might not be possible. And I don't want to spend much more time than necessary on GtkIMHtml.

Add space between ) and { in all ifs.

Add surrounding braces.

Ship It!

Amazing work, thank you so much for going through so many iterations and seeing this through until the end!!