Most horses live to eat, even if they are not underweight. My guy does not have a 'stop eating' button. :)
How many meals is she getting per day? From the sound of it, she's getting about 2 1/2 flakes of alfalfa and an hour of grazing a day, which is not nearly enough for a horse that needs to gain weight. I would work her up to grazing a few hours a day and 10-15lbs (maybe more) of alfalfa per day over a couple of weeks. Let her eat all the hay she wants once she can handle it. If at any point as you're working her up she gets loose stool again, back it down a little and hold it there for a couple of days before working up again. One acre of pasture really isn't that much, so if you want to keep it nice for her, consider learning about pasture management.
One she's on all you can eat hay, if she's still not gaining weight, consider adding grains and/or products like oil, cool cals, ultium, etc.