I can explain the tradition of the garter, and trust me, the original was a LOT worse.
In medieval times, after the ceremony, the bride was taken to the bridal chamber and stripped naked by her female family. A few moments later, the groom entered with the male members of the family. He too was stripped naked, but the bride's assets were shown to all the guests, while the groom's were not.
It was a visual verification of their wedding night (and assumed consummation) and of the bride's physical offerings.
Eventually, this decreased into the garter. Also, it was common to place the bloodied bedsheets over the fireplace in the main hall, to prove the groom's virility and the bride's virginity.