on first look she does look preggo!... and they usually carry on one side and shifting seems to be the norm with that. check to see if she is bagged up and what her teets look like.
but if there is no possibility of that ...i have known a donkey that had a massive fat deposit on his crest it actually hung to one side. but since this shifts sides this seems unlikely.
if she is that fat...adding some chromium and magnesium to her diet could help ( i know it helps with fat deposits)...
*Member of the Quality Free-Choice Hay/Pasture Feeders Society* *In Favor of Turning horses out as long as Possible*