I think I know what the OP is referring to.
There used to be, and maybe still is, a “Timmy Fund” for developmentally handicapped kids* in Ontario (perhaps all of Canada). It’s easy to see a possible connection (for people from Ontario at least) with mentally retarded. In fact, my clique used the expression Timmy in the same context as the OP suggests. That was almost 40 years ago! Way before South Park.
Haven’t you seen any old Lassie episodes? Timmy was such a stupid little stumbledrooler that he just kept on falling down mineshafts and getting stuck in chimneys and getting lost in his own backyard and so forth, week after week, even though he did have the world’s most intelligent and eloquent dog as a bodyguard, babysitter and rescue service. 
The name’s been tarred with the tard brush ever since. 
Finneas (may be slow to load - be patient).
That could be true, because I don’t know anyone named Timothy who goes by Timmy. Usually it’s just Tim.
My cat ran away once, and the woman who took him in re-named him Timmy. I thought that was kind of an insult; he’s a smart cat.
I think I remember watching those late night infomercials when they were in there proto form. The lady who plays gloria in All in the Family usually had some little urchin in her hand that she was shilling for ,and she probably had a timmy or two.
Declan
I have noticed in my own noticings that many mentally handicapped males never get “grownup names”. They’re not Jeffrey or William or Timothy but always the diminutive “Jeffy, Billy, or Timmy”.
The head of the Special Olympics is now Tim Shriver.
Just one of life’s little coincidences.
IMDB is your friend.
