Umberto Eco wrote an excellent book called The History of Beauty, in which he categorizes the different ideal body types as the nude and clothed Venus and the nude and clothed Adonis. The Adonis tend to follow the Classical ideal of the athletic figure, while the Venus-types range from the Venus of Willendorf (the prehistoric rotund little woman with huge breasts/hips to emphasize her fertility) to more (relatively) skinnier figures of the Classical and medieval periods, to more fuller-figured in the Renaissance...really it varies, depending on the ideal beauty of the time as well as the stylistic inclinations of the artist.

That only deals with Western art; as far as Eastern goes, I do not have a source for this but I believe that in China the ideal for the nobility was to really show that they didn't have to work, hence the bound feet, extremely long fingernails, and being heavier/better fed than the average peasant. But being better fed would have been true of the Western world, too, simply from the reality that the nobility would have had much better access to protein, fat, and sweets, and also regular access to food than the rest of the world.

The bottom line is, male figures tend to follow the Classical athletic look, while female images tend to have more le-way depending on personal style. There are, of course, exceptions - Michelangelo's work in the Medici funerary chapel comes to mind, where his statue of Dusk (or was it Dawn?) looks like a male figure with breasts added on to make it female. In a similar vein, Eco's "Clothed Adonis" examples include some fairly Romantic images of men, which take a different approach to masculinity by emphasizing the internal, as opposed to external, personality traits.

I am by no means an expert on the area, but during prehistoric times, notably in the Western European stone ages, there seems to have been a cult centred around a large breasted, large hipped female figure. The evidence of this are the various figurines called the Venus figurines. These date from 40,000 years old to around 10,000 years old. Areas of the body associated with fertility and child bearing, the breasts and hips, are exaggerated in these statues and the figure depicted would be called 'obese'. The head and legs are the figure are periphery to the main focus, the torso, and it can be inferred that these traits were desirable in that society. The most famous of these statues is the Venus of Hohle Fels if you want to have a look at it yourself on wikipedia.

Statues from later periods, such as the Classical and Hellenistic Greek world show Aphrodite or Venus in more human proportions. Examples such as this and this show that wide hips were desirable, though the prominence of the breasts is down played. It's a classic hour glass figure with the fullness of the figure perhaps a little larger than what our society would call desirable today.

Bypassing all of recorded history we find adverts trying to sell weight gaining plans for women in the late 19th and early 20th Centuries. Examples of this are here and here. Though there are examples of weight slimming plans, such as this, which do show that there was such a thing as too big.

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People often use the argument you laid out in your question to mask their own insecurities. With the high rate of infant and mother mortality in previous times wide hips were a boon to childbirth. With the rise of modern medicine these notions have been disavowed for the most part. While it is true that larger figures were seen as more attractive the largeness of these figures should probably not be over exaggerated.

Social considerations, such as wealth and status, do not seem to be bear as much consideration as the health one. Paintings from the medieval period, such as by Breugel, who is notable for painting peasents and the lower classes much more frequently than others, do show large, full figure women. It is possible that skin paleness, with paler being better for women, showing that they did not work outside, is probably something which haws more closely to your questions about social status, wealth and appearance.

I think you're inappropriately equating desire with beauty, and you're also being very non-specific.

I think the way to phrase this question is, "Was weight regarded a sign of wealth and considered an attractive quality in X era?"

If you narrow this down, we might be able to help you a lot better.