Steve, the transcription of the 1880 census into machine-readable form is not yet complete; so far Arkion provides only some Norrland counties for 1880 online (and perhaps some others I didn't notice, but Stockholm is not among them). Thus you would have to wait for an 1880 census search to be meaningful, perhaps a few years (the 1900 census is not yet complete either, but somewhat closer).
I have also considered the possibility that he didn't go by the name Blomqvist in Sweden. However, if he adopted it upon emigration only, would he then really identify his father (who supposedly remained in Sweden) as Charles Blomqvist in his marriage license?
While Blomqvist, Eriksson, Karl and Sofia are all fairly common Swedish names, I hope their specific combination may turn out a bit more useful. The 1890 census includes 14 Carl/Karl Blomqvist (exact spelling) and 5 Sofia Blomqvist, although I suppose that your Sofia would be listed under her maiden name rather than that of her husband. Allowing for alternate spellings and additional first names yields a few more possibilities, but I think it would still be possible to work them through systematically and find out which Karl Blomqvist's were married to one Sofia.
I haven't attempted such a systematic search, but by spending 15 minutes with the 1890 census at the library I found one Karl Anton Blomqvist born 1843, married to Gustava Sofia Selander born 1834, living in Adolf Fredrik parish (in Stockholm). I doubt these are your Charles and Sofia, and therefore I don't suggest spending any time on them yet, but it demonstrates one way of approaching the problem. However, the method does require both parents to be still alive, married, and living in Sweden in 1890, which need not be the case. For all we know, Karl Alfred may have been orphaned even before emigration.