The Sages have said:

In the Code of Jewish Law1 it is written that a Torah scroll should be held in one's right arm (and rested on the right shoulder). This applies even if the one holding the Torah is left-handed. There are two verses that allude to this idea:

1) "From His right hand was a fiery Law for them" -- Deuteronomy 33:2. The Torah was given from G‑d's right hand, as it were, and we therefore hold it in our right hand, too.

2) "And His right hand will embrace me" -- Song of Songs 2:6. G‑d embraces us with His right hand, and we, in turn, embrace His holy Torah with our right hand.

— Rabbi Yisroel Cotlar
http://www.chabad.org/library/article_cdo/aid/571210/jewish/In-what-arm-does-one-carry-a-Torah-scroll.htm

The Sages have said:

What is the cause of the mourning (Zechariah 12:10)? It is well according to him who explains that the cause is the slaying of Messiah, the son of Joseph, as it is written, 'And they shall look upon me whom they have pierced; and they shall mourn for him as one mourneth for his only son.'

— Babylonian Talmud
Babylonian Talmud, Sukkah 52a