Well...there are different types (species) of the mustard plant.
https://en.wikipedia.org/wiki/Mustard_plant
Frankly, I'm not sure what you mean by "mustard weed", but I'm guessing that it is, in fact, a species of mustard plant
http://www.ipm.ucdavis.edu/PMG/WEEDS/mustards.html
Almost certainly *not* the same species to which Jesus was referring (a domesticated species).
P.S. This article addresses the Biblical "bird-supporting" mustard plant:
http://ww2.odu.edu/~lmusselm/plant/bible/mustard.php