Obese people have so many health problems that we have to pay for. Skinny people have less health problems. Also skinny looks better than fat and it's healthier to be underweight than overweight. Seriously--heart disease (my dad's skinny and he has heart disease because of genetics so not all people with heart disease) cancers (caused by obesity).
In many countries, particularly first world countries. We are constantly bombarded with facts, reminders and consumables in favour of preventing obesity. We are constantly reminded that obesity can lead to heart disease, diabetes and many other health scares. In addition to that, many celebrities and models are thin and many criticized by the media for not being 'thin enough'. There are also ample advertisements for weight loss medicines, diet plans, workouts etc. However, you seldom are bombarded with reminders of the dangers of being underweight (such as infertility in women, osteoporosis etc). It seems as though our society is more focused on how intolerable it is to be obese, perhaps because as the headline states; obesity is an epidemic, at the moment.
Socially, the answer is (surprise, surprise) 'yes'. It is a matter of how our society perceives weight, which right now, is a matter of being as thin as possible. While obesity is a rising epidemic, the number of anorexia cases has increased dramatically over the last few decades, as have other eating disorders (e.G. Bulimia).
Note that this question says underweight rather than thin. Being slim is generally a good thing. It is a sign of taking care of one's body, but being underweight is different. It could be the result of health issues or eating disorders. I feel like it is equal with being over weight. However, in society today, I see underweight people being shamed a lot more than overweight people. I am a slim (but healthy) person, yet I have been criticized and looked down upon for being too skinny. If I was legitimately underweight, I think that would worsen the problem. Since more people are obese (or even just overweight) I think that they often look down upon those who are underweight or even just slim to try justify their position. In reality, being underweight and overweight are equally bad.
Using a BMI chart, I am listed as slightly overweight. This is because muscle is not factored into the equation. I spent most of my pre-teen years exercising in an attempt to reduce my weight but just keeps moving further along the chart. I am only 16% body fat, not every person on that end of the scale is obese. Usain Bolt is even considered overweight. During sporting events, I'm actually preferred to someone half my size and half my speed, and strength.