Ok, I don't want to scare you, but this really, really sounds serious. Almost 3 months old and weighing that little.
Him not having an appetite, being so little and being sluggish, etc...
I would really, really be concerned that this little fella may have liver issues - either Liver Shunt or MVD
I would get him to a VERY GOOD Vet - one that has experience with Small Breeds (preferably Yorkies) and get on top of this ASAP.
LS/MVD dogs usually are very picky eaters b/c the 'wrong' foods are given to them, foods too high in protein cause toxins to build up in them making them feel sick, hence they don't want to eat
I wouldn't be taking ANY chance with a 3 months old weighing that little and
with the other symptoms, etc...
PLEASE KEEP US POSTED