Has there ever been anyone who forbid interracial marriages when the girl is caucasian and the man is black on Halachic grounds?
Halacha recognizes the difference between Jews and non-Jews. "Race" is such a hard-to-define concept that it would be pretty much impossible for any laws to exist in such general terms. You really would need to explain what you mean by "interracial" for us to give a concrete answer, but I would imagine that in any case, the answer to your question is that nobody forbids it.
Jews are allowed to marry Jews. There is no argument that some Jew could not marry another Jew because of his/her race. As far as non-Jews go, I really don't think that any restrictions exist besides the already-mentioned restriction that Jews should not marry non-Jews (I am not sure who the onus is on there) and the restrictions laid out in Leviticus about forbidden relations (e.g. between two men or between close family members, among other examples).
It is not entirely unlikely that some Jewish leaders more than 50 or 60 years ago in the United States opposed interracial marriage, as that type of relationship was frowned upon by a significant portion of the American population at that time; however, I have never heard of any halachic arguments to justify such an opinion in general, nor can I think of any.
There's a book of very old responsa of the Conservative movement where this question was asked about a hundred years ago. (I assume the answer was that it's permissible.)
As the comments point out, Jews are supposed to marry Jews; but there are Jews of every color.
The question is pretty open-and-shut, however. Tendler and Loicke have an essay on defining humanity vis-a-vis Jewish law, but even without that, if we were to apply the laws of cross-breeding animals, the Talmud gives a few criteria for determining that two species are in fact sub-species (and therefore may be cross-bred); e.g. gestation period and mating behavior. I am allowed to breed any type of dog (but not wolf) with any other type of dog, for instance; so all the different "flavors" of Homo sapiens sapiens would be recognized as one species and therefore pose no problem of cross-breeding.