What is big about the earlier mincha time and what is small about the later mincha time? Also, why does the term plag mincha make sense? It would seem to be a term that refers to the point midway between mincha gedola and mincha ketana, but it really is the midpoint between mincha ketana and shkiah (sunset).
Mincha Gedola is three hours long thus it is the big Mincha. Mincha Ketana is 2 1/2 hours long thus it is the small Mincha. Regarding Plag Hamincha it is the time in between Mincha Ketana and Shekiya, which is half of the time of the Mincha remaining. It does not mean the half time between the two Minchas as there is no Halachic significance to that time. However there is halachic significance to Plag Hamincha which is between Mincha Ketana and Shekiya, regarding how early one can make Shabbos, regarding according to some to Daven Maariv already.
וקראו למנחה הראשונה 'גדולה' מפני שזמנה ארוך יותר – שלוש שעות, והשניה שזמנה שעתיים ומחצה נקראת 'קטנה'
According to the Schottenstein Edition of Berachos, 26b2 note 24, "the earlier portion, called mincha gedola, "greater minchah" [because the greater portion of the day remains -- see Perishah, Orach Chaim 232:5], and the latter portion, known as minchah ketana, "lesser minchah" [because only a small portion of the day remains]."
The gemara there (as noted by the ntes 28 and 29 on 26b3) discuss plag mincha achrona and kama and how the plag, half-way mark, depends on if you mean plag of gedolah or ketana.