I tried using "heavy" instead of "fat" and it was marked as wrong! In the dictionary, kövér is also defined as "pudgy, plump, overweight, corpulent, beefy..." so I indicated that "heavy" should also be accepted.
I remember the adjective because kő = stone and vér = blood... someone whose blood is made of stones would be very heavy / overweight / fat, indeed!
Depends on your needs. I have the akadémiai kiadó szótár. It is the most complete I have seen so far, but it may not be suitable for everyone. Word meta information uses hungarian abbreviations (which are easy enough to learn). It is split into two books and also very heavy, so not suitable for travelling. I also have the hyprocrene dictionary by Eva Szabo from amazon. It is smaller and only a single book. It is far more suitable for travelling, but I had pages falling out quickly after buying it. The binding doesn't seem to be very good. It is not nearly as complete and you might need to be more flexible when looking up a word, for example looking up the associated verb or adjective of a noun, because the noun isn't in there.
None of those words actually MEAN heavy. Overweight kind of comes close, but is still not the same. Someone who is fat, is heavy only by logical derivation. It is not an accurate translation, because there is a shift in emphasis from the body shape to the weight. Someone who is heavy is not necessarily fat. They could be a body builder. Or they could simply be wearing weights. Even if the word is made up out of stone and blood, that doesn't mean a thing, since it is a word in its own right. The translation "Stone blooded men are not good actors" does not make sense.