Haha! The word "gravity" also means "seriousness", though (http://www.oxforddictionaries.com/definition/english/gravity), so it could be used in a medical context: "The doctors were aware of the gravity of his illness".
Well, in fact yes, there is a Connection if I could translate literally this phrase ... "a gravid uterus is pregnant" would be "um útero grávido está prenhe". As we can see "gravid" and "pregnant" both words have different etymological origins for the same meaning, but in english is common to use the word "pregnant". In Brazil we use "grávida" for women only. The "pregnant" term (from Latim PREGNANS) has became "prenhe" which is used for animals only. Despite these words coming from the same radicals they generated new words that have been modified over time with daily use in every language and started to produce different words with different meanings. So... back to the major point (about gravid term) the prefix "gravid" generated the nouns "gravid.ade" (which took the meaning seriousness) and "gravid.ez" (which took the meaning full, abundant) Then "gravidade" can be "something grave" or "seriousness" or "gravity", but will never be pregnancy (gravidez)