It s a fern.....so not exactly a weed :-) I am not familiar with what species grow in your area but few are considered weedy. It has likely established a colony in the wooly surface of the palm trunk but it is not harmful to the palm at all and does not need to be removed.

Fern spores (several species of them) sprout in the crotches of palm fronds because they like that environment. I don't know how well ferns respond to Round-Up, but if they do that would be one way to get rid of them, so long as you're careful and don't get it on surrounding plants. Or you could remove it by hand the same way as pulling weeds. It will be ongoing.