I’ve got a problem myself as well.
My friend commented on something saying only “Specially for you”. Underneath it became some sort of trollbattle using Especially or Specially for you.

Now I’m confused. Anyone knows which was right one?

Oh I’d like to say something about English/writing forums or sites. I find it amusing how pretentious everyone sounds when they disagree on a particular topic. I know no one is trying to be pretentious, Hell I may be coming off as pretentious right now. I just find it amusing. The thing I dislike is when people feel the need to insult someone who doesn’t use the proper syntax, misuse of a word, or a spelling error. I know that this and others like it are about proper English and I can see why they would point it out. However there is no need to insult the person. On sites like youtube or facebook there is no purpose for that behavior. We are on the internet not in class. So unless the person making said error is writing an article just let them be.

Sorry for veering off topic, I just felt the need to put that out there for some reason. Maybe I felt that way because I was just on youtube and the trolls were irritating me. I refuse to feed the trolls, so you all had to suffer my complaining. I already typed it so I might as well post it. Again I apologize.

-His train was running especially late that day.
-We were especially happy to see you.
-I put the cake especially high.

They all mean “more than usual.”

Consider an alternative example:

“The plutonium was placed in a specially designed container.”

The container was not “more designed” than others. It was designed for a special purpose.

However, we can also modify a phrase:

“The container was designed especially for holding plutonium.”

Then I would certainly use especially.

Compare:
-This building is not especially tall.
-This building was not specially designed.

I admit that to me a sentence like “This reactor had to be especially designed” sound like nonsense. As though it had been “VERY designed.”