Arabic حلاوة (=halawa) and حليب(=haleeb) don't have same root grammatically. However in deep historic arabic grammars maybe there is 'B to V' changes there too. (there is simillar concept in this case in Persian language too, Sheer (شير) means milk and Sheereen (شيرين) means sweet. And ين suffix means 'similar'. So شيرين also means 'similar to milk in taste'.)
I hope this helps :-)
1st if you are talking about old arabic(arabic spoken by prophet ismail son of abraham peace be upon them) wich is the earliest form that is close grammatically phonologically and lexically to modern standard arabic has been since 1000 century BCE. Not mentionning the proto-arabic that is earlier of course.
2nd the old hebrew is since 1600 BCE. So not that much difference in time, plus both languages has developped independently.
3rd if you are talking about classical arabic is since 3th BE, and MSA reform is in 19th to add new scientifical terminoly and those terminology are tooken from english and french. So nothing has enterred arabic from hebrew.
4rth modern herbrew have been reformed by eleizer ben yahuda in 19th that took too many arabic based words, so indeed herbrew has lot of arabic in it.
That without mentionning the golden arabic age that affected asian african and europian languages that the last, then, affected hebrew, exp: sofa(صفة) , camera قمرة، alcohol, الكحول, alogarithm الخوارزمي, algebra الجبر, magazin(french) مخازن, food like sugar(سكر)/artichoke(ارضي شوكة) , barut/gunpowder (in turkic/iranian/solvic languages) بارود, sunduk/chest (russian/turkish) صندوق. And a much more from the 1st pharmacy in the world in iraq to the first accurate way in doing surgeries to the 1st appearance of the physics of light, the arabic numbers ( 1,2,3....).
Of course there are lots of commun grammar features commun words between the 2 languanges including sugar(sukkar سكر) (that as i mentionned, it is through arabs that this word was spread), soap(tooken from greek (σαβον savon) that itself tooken from semetics (saboon صابون), and much much more that arabic learners would notice.