Carrying the bride across the threshold is a common practice, not only in the English speaking world, but in many other countries as well. To understand this you need to go back to the origin of the threshold itself.
In ancient times, most houses had mud floors which would get slippery and messy from the rain water that was carried in on the shoes and boots of people going in and out of the house. To counter this, straw (thresh) was laid on the floor. Inevitably, the thresh would spread and creep through the doorway, so a wooden bar was laid across the doorway to hold back the thresh, hence threshold.
On entering her new home, the bride had to be careful not to trip or stumble on the threshold, as that was a bad omen, signifying that the marriage itself would fail. To avoid this, the groom would pick up his bride and carry her safely over the threshold.
It apparently did not matter if he tripped over his own threshold.
Of course, there were dangers, as when the bride was heavier than the groom, and it could be that some negotiation had to take place.
So the practice of carrying the bride over the threshold was by no means either obligatory or universal. However, it did add a gallant touch to the end of a wonderful day.
There is another version of the origin of this practice. In Roman times, a bride had to demonstrate her reluctance to surrender her virginity. So she had to be carried over the threshold, lest she should run away.
She may not have been reluctant at all, but it was necessary, for the sake of decorum, to pretend!
There will be more stories of myths, legends and customs here, if you keep looking. Meanwhile, if you’d like help with a speech (for a wedding or any other occasion), drop a line to firstname.lastname@example.org.