A lot of Manhattan apartments are in converted factories. With the wheels, the box looks about three feet high. A maintenance man may have adapted it as a combination scaffold and tool chest. The sideboards appear to be a foot off the floor. They would help a worker step onto the box and serve as foot rests if he used the box as a high seat.
The slots suggest it was made for something with a shaft. The doors suggest that the shaft was removed before they were closed. That sounds like a beam for a loom.
Patterson, the world's silk capital, was 20 miles away. For cotton and wool, the world's biggest mill complex was 150 miles up the Hudson. An apparel manufacturer might pay top dollar for a single roll of cloth woven to his specifications on a quick turnaround. A mill might not even accept an order for one roll.
I see a market for small weave shops in Manhattan. A mill would gladly wind beams for them as they would not be competing for large orders. A weaver would keep several beams of different color patterns on hand. At the mill, the 836 may have told a foreman what pattern was to be wound on the beam. The D may have told him what weave shop it was to be shipped to. At the weave shop, the weaver would want to know which end of the beam was which so that the box could be properly positioned at the loom before it was opened. The H door may have identified the head end of the beam.