The jack capacity has to do with the tongue weight of the trailer, not the total weight of it. In theory, even a 1500# capacity jack is enough for any AS, but in practice those numbers are pretty iffy. The real low lifting capacity units are pretty marginally made from what I have seen. You also may be using it to lift the rear of the TV to hook up chain bars and that requires more lifting capacity than the simple tongue weight would indicate.
That said, probably I would buy a 2500 # capacity jack. BTW, some are bog slow to raise and lower, and there is no way to predict that without using one just like the one you wish to buy. More lifting capacity does not mean faster either. If possible, and you are buying locally, see if they have one on a rig you could try out. Listen for how it sounds.. is it smooth, does it grind, click, clack and clunk, how fast does it go.
And lastly, unfortunately the models and where they are made has changed a lot in recent years due to financial pressure. So, advice from others about their jack may or may not get you the same jack today. A good dealer can help you out here, ask about how many have been returned, and what they think of the unit. With luck you may get some good honest answers as to what is a good one today vs. ones they are not happy with.