In Patrick Stewart's version of A Christmas Carol, the overweight Mrs. Fezziwig claims to be on a diet after being called out on eating by Mr. Fezziwig.
Would anyone from that period think of "a diet" as a restriction on caloric intake to lose wright, or that being overweight was even a problem?
It depends - the thing about "overweight" is that it's dependent on what your culture considers the proper weight. In the 19th century, the fashionable/acceptable body type was heavier than it is now, for both men and women, with a graceful roundness to the face, limbs, and body being prized and angularity considered unattractive. Some recommended that thin women not wear smooth, plain silks, which would not "fill out the bony skeleton". At the same time, being too large was considered a problem. For men, having a waist measurement equal to or greater than the chest measurement counted as stout enough to require alterations from the norm in tailoring; stout women were advised to avoid both vertical and horizontal stripes, very light colors, and puffed sleeves.
Exercise was recommended for both the stout and thin. Doing side bends was supposed to keep the waist both round and delicate; other drills would make the arms and neck rounded. Thin women could gain by eating carbs and fruit and drinking milk, while a fat woman could lose by eating greens and bathing in salt water. On the whole, the popular conception of being over- or underweight appears to have been related much more to aesthetics than to health. Paying attention to calories and caloric intake specifically did not come about until the rise of domestic science late in the century. It was fairly entrenched in society by this point, however, that women should/did eat much less and lighter food than men - that ladies were inherently more interested in the aesthetics of their food and should require little sustenance.