Megillah Leining (מוצש"ק)
In Meseches Sofrim (14th Perek) it says that the Minhag is to read the Megillah the first two Motzei Shabbosos before Purim.
The first Motzei Shabbos in Adar you read till בלילה ההוא. The second Motzei Shabbos (tonight) you start from בלילה ההוא
till the end.
It is unknown the reason or the source for it.