I've seen these particles used in a metaphoric sense, where a fantastic, implausible scenario is presented for effect:
Тебе, наверное, женщины на шею так и вешаются.
Он так и покатился со смеху.
In these cases in English we say The women must literally be throwing themselves at you, or He was literally rolling with laughter. However, I've also seen так и used with plausible situations, but with somewhat "extreme" verbs that describe things the subject is prone to do, yet to a higher, degree:
Дождь так и льёт.
Солнце так и жжёт.
Ветки так и гнулись под тяжестью яблок.
These make perfect sense to me as I assume they mean The rain was absolutely pouring, or *The sun was absolutely sweltering*, or *The branches were literally bending under the weight of the apples*. However, I was hard put to interpret this same "extremeness" in the following sentence.
Кошка так и ластилась к его ногам.
In what situation would somebody say this and what would they mean?
как+ perfective verb in future tense" means that the action happened very quickly and often unexpectedly. Thatкааакis usually pronounced with intentionally prolongedato prepare the listener, and then follows the verb, pronounced quicker and louder, with emphasis. Here the action happens only once and is completed, that's why perfective verb is used. If the action is repeated multiple times and/or is not completed, than "так и+ perfective or imperfective verb in past tense" can be used. For example,Она так и запрыгала от радости("She started to jump with joy"). – Lara Dec 30 '16 at 20:01