The baggage comes from the old practices that underlie the common expression. Once upon a time a father in effect owned the daughter, and almost in a literal sense "gave" her to the future son-in-law. As Leslie said, that's not what Steve meant to suggest, but the connotation is still present for some, maybe a lot of people.
Giving Your Daughter Away.
The tradition of the father giving away his daughter has its underpinnings from the days of betrothals and arranged marriages. Daughters were considered their father's "property: and it was the right of the father to give his child to the groom. In some cultures, the groom "bought" his right to the bride.
Thankfully, times and cultures have largely changed, but the tradition continues a symbol that he approves of the marriage.
Not every father and daughter will want to have this part of the ceremony, although a father walking his daughter down the aisle is a well accepted and sometimes touching part of the ceremony.
Now, it will seem like you, Dad, are putting your daughter literally and figuratively into the arms and care of someone who is barely ready to accept the responsibility. But it is a wonderful gesture of confidence in your new son-in-law, and should be done graciously.