I'm a bit confused as to what this やっぱり is doing in the sentence above.
やっぱり has several meanings, such as:
- やっぱり、思った通りだ。 -- It is so, just as I thought/expected/suspected. -> That's exactly what I thought. / I knew it.
- やっぱり、こっちにします。 -- On second thought, / I changed my mind, I'll pick this one.
- それでも / なんだかんだ言っても、やっぱり嬉しいです。 -- But I'm happy, nonetheless / all the same / after all.
Here in your sentence, I think it's used as the 3rd meaning, "nonetheless, after all, all the same".
Because it makes me realize you think of me so much... after all / nonetheless.
やっぱり is frequently used when someone is uncertain about what to do or how to feel about something. For example:
Maybe I should go to England. No, actually I'll go to Japan!
Regarding your dialog, without the full context and knowing what they are talking about, it is hard to say for certain, but here I get the feeling that the person saying "やっぱり" was sort of indecisive about something and now has decided a bit more firmly. Or possibly they just thought about something for a second or two before deciding their stance on it. I think colloquial use of "actually" contains some of this feeling.