Shalom:
Good question and thanks for trusting me with the   answer.
We of course don't wish folks a 'happy new   year'.
We wish them a Shana Tovah, a good   year.
So where does sweet come into play?   ["u'metuka"]
Well first, we need to remember that there are 4 Jewish new   years.
The one this Monday, is on the first of the 7th   month.
It is the New Year for not Jews, but for humanity, because Adam and   Eve, so we teach, we born, created on this day.
And the Jewish people's New Year is on the first day of our first   month, Nissan.
And we celebrate it 14 days later, as Passover, when we were born   as a free nation.
And we say then, have a sweet   Passover.
So the sweetness got carried over.
The other new years, are first of Elul which is for animals, and first   of  Shevat,   moved to the 15th of Shevat, by Rabbi Hillel, i.e. Tu B'Shevat, which is for   fruit growing trees.
Now for sweetness: it is a bit like which came first, the chicken   or the egg.    
We eat an apple on Rosh Ha Shana. The apple symbolizes Gan Eden (the   Garden of Eden), which according to the Talmud has the scent of an apple   orchard, and in Kabbalah is called "the holy apple orchard."   Isaac commented   regarding his son Jacob (Genesis 27:27), "Behold, the fragrance of my son is   like the fragrance of a field, which the Lord has blessed!"   The Talmud explains   that this refers to the scent of an apple orchard, the scent of Gan   Eden.
There is a deeper meaning happening here. Rosh ha Shana, Yom Kippur, etc,   is a time when God forgives us for our sins to God. (For sins to humans, we must   make amends to them).  When we eat an apple we are reminded that God forgave Adam and Eve, and   that for Jews, there is no such thing as 'original sin.'  We have   freedom of choice. We can choose to do good, or not. And if not, the Talmud   teaches God 'invented' teshuvah, repentance, spiritual renewal, before he   created humankind. So we eat an apple to remind us that if we sincerely do   teshuvah, ''the gates of teshuvah are always   open.''
So apples are sweet. The spiritual lesson of the apple got lost over   time, and so we want our year to be sweet like the apple.  And we eat other   sweet things, and avoid bitter things, (no horseradish with the brisket, no dark   foods like chocolate or eggplant, to remind us of death).   Coupled with the   added sweetness of the honey, it is symbolic of the ultra-sweet year we hope God   will grant us. Life is sweet. Death is bitter. 
Remember, this is a time of being written into the book of life, or   not.
When Solomon depicts the love God harbors for His nation, he writes (Song   of Songs 8:5): "Beneath the apple tree I aroused your love.'' Eating an apple on Rosh   Hashanah is an attempt to remind us that God loves us, and we hope He will treat   us sweetly, kindly, goodly, this   5777.
Jewish Spiritual Renewal
Jewish Renewal
Jewish Spirituality
Hilton Head Island, SC; Bluffton, SC; Savannah, GA

