With time or By time?

Even though "by" can mean "during the course of", I believe that it is used only when the time is specific. For instance you can say "I'll do the studying by night", but not just "by time". It can also mean "by the time", this again indicates some specific time frame. Whereas "with time" implies "given enough time. So I believe "with time" is the better word-choice at this scenario. There is also the possibility of writing "in time". While it also kind of expects a specific time-frame it can be more abstract than "by time". For instance "In time you will come to realize that..."

Students' vocabulary knowledge is a building process, which occurs over/with time, as they make connections with other words.