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Is there a reason/meaning behind the "half-brick over brick" layout of Shiras Hayam as written in a Sefer Torah? I am familiar with the gemara in Megilla (16b) that states the layout is to be that way, but I would like to know WHY.

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I was honored with that aliyah today and it struck me, while looking down at the scroll, how much the text looks like waves. (This is more prominent in the sefer torah, where the ink floats slightly on top of the parchment, than it is in a printed edition.) I don't know if that's part of the reason or just a side benefit. –  Monica Cellio Jan 26 '13 at 23:48
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There are two special layouts for songs - half-brick over brick, and half-brick over half-brick. The half-brick over brick is triumphant and good. The half-brick over half-brick is bad - bury the sons of Haman or the sins of the Jews.

Megillah 16b that you reference says:

‫אמר רבי חנינא בר פפא דרש ר' שילא איש כפר תמרתא כל השירות כולן נכתבות אריח על גבי לבינה ולבינה על גבי אריח חוץ משירה זו ומלכי כנען שאריח על גבי אריח ולבינה על גבי לבינה. מ"ט? שלא תהא תקומה למפלתן.

Rabbi Tanina bar Papa said that Rabbi Shila, leader of Kaper, taught: All songs are written a brick over a half-brick and a half-brick over a brick except this shira (the sons of Haman [Ester 9:7-9]) and the kings of Canaan (Joshua 12:9-24) which are written a half-brick over a half-brick. What is the reason? So that they should never rise again from their fall.

(Aside: Somewhere, though I couldn't find the source, the Ritva says that "this shira" means "all shirot that are not about praise" so that it includes Shirat Moshe in Haazinu.)

Rashi there says:

‫ שלא תהא להם תקומה - שלא יהא להם מקום להרחיב צעדיו תחתיו:‬

So that they should never rise - There is no place to expand their footsteps.

But that doesn't answer why for the good shirot.

The Maharal explains in his commentary there:

‫וזה כמו שאמרנו: כי גברו ישראל והתפשט כח שלהם ביותר. ולכך השירה הזאת היא אריח על גבי לבינה כי זה מורה התפשטות לפי שהם מונחים בענין שיש להרחיב תמיד. וכך כאשר ישראל מקבלים שלימות אין זה הוא התכלית שאי אפשר שיהיה עוד רק הם מוכנים להיות להם יותר שלימות. אבל השירה הזאת היא אריח על גבי אריח כי השירה הזאת בשביל שהפיל שונאיהן שלא היה לו תקומה כלל. וזהו נפילה גמורה שהגיע למפלתן של רשעים.‬

And this is like we said: that Israel became mighty and their strength spread out. And so this song has a half-brick on a brick because it shows with this placement that there is eternal expansion. And thus as Israel attains perfection, there isn't this idea that it is impossible to be more than just what they are. They are prepared to be more perfect. But this song is written half-brick on half-brick because this song is for the sake of the falling of its enemies that don't have a way to ascend at all. And this is the complete descent which is the downfall of the wicked.

Taken together, the Maharal and Rashi seem to me to picture the "half-brick over brick" style as a staircase or lattice-work you can climb to greatness, whereas the "half-brick over half-brick" style is a pit without a path up.

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