Welcome to the forum!
And, yes, it will weep down from where it is grafted unless you train it up higher. It will eventually spread out more, but it will not get incredibly wide, either.

However, it is NOT slow-growing. It can grow in excess of 12" in one year.

To give you an idea of their mature habit, here is a picture of me a few years back standing between some very old specimens that appear to have been allowed to reach about 7 feet in height at Iseli Nursery. From there, they simply hang down gracefully.

-Sam

Trees shown are 'Reflexa' and liable to be same as original poster is asking about. The 'Pendula' of general commerce is 'Reflexa', and as the Iseli examples demonstrate is more inclined to recline than climb.