Pretty girl you've got there!
I too don't know what goat head is, and never heard of horses eating mustard weed. As Smilie said, weeds can be a problem & horses don't always know what's good for them(I've heard horses won't touch capeweed unless starving, but my horse LOOOVES it!), but perhaps your local ag advisor, or vet or such will know whether goat head is a problem or not. Remember, a 'weed' is just a plant we don't want growing somewhere at the time - not necessarily bad.
Agree with getting professional advice & poo checks for the worming. Agree that the horse could be lacking in some nutrients, which may explain her eating 'weird' weeds. You say you're feeding her 'vitamins' but what vitamins? & are you supping minerals as well? And how do you know what vits & mins she needs/is lacking in? Not the best idea to just supp stuff without good reason.
Yeah, she does look rather fat, but if this is short term, no stress. If she's kept fat long term, that's when she's most at risk of it causing health issues.
And a couple other 'asides' from the pics... please do not tie up a horse solid to that kind of a fence, or anything else not strong enough to withstand a panicked horse! She may well be well trained & calm, but accidents can happen very easily(& terribly, when you end up with horses running around with sections of fence attached to them!), so ensure that if you tie solid, tie TO something solid, or use baler's twine or something that will break first, if there's an 'event'.
And it appears that saddle is quite a bit big for her, will be hurting her back. It appears that it is well over her shoulders - should sit behind her (extended) scapula - but it is already over her loins too far, so can't just be placed back further. I love western style saddles personally, but they are longer treed, for seat size, than English style, so often just not suitable for short backed horses, if the butt in the saddle is a med or large!