In case anyone is still confused: The difference is like an event in time (marra - مرّة) versus the general concept of time (wa2t - وقت).
In English, we say "how many times..." to represent countable events such as, "How many times did he repeat that word?". In this case, you would use marra, because the event is countable. Consider how awkward it sounds to say "how much times did he repeat that word?" in English.
On the other hand, when referring to time in general, wa2t is used. This refers to some unspecified amount of time or even to time as a concept. Because it's uncountable in English, we say "How much time". If you find yourself saying "how much time" or a more abstract concept like "time of ____", then wa2t is almost definitely what you need.
For example, in Haifa Wehbe's lullaby Lamma ash-shams tirawwah (When the sun goes down), she sings:
yib'a il-wa2t dah eh? -- That time is [becomes] what?
yib'a da wa2t in-noom! -- This is the time of sleep!
In other words, when sun goes down, it becomes "sleepy time". This indefiniteness of time is translated using wa2t.