Portraits are quite a difficult thing to master and to understand them we have to look into their context first.

Portraits were used for many different reasons and some were even made in different moments of a person's life and for a portrait to be successful the painter had to master the following:

1. Notions of taste: a) First and foremost, in art. This could be conflicting, sometimes, as the nobility and the royal family would often invite foreign artists to do their portraits and they had to adjust to the artworld from where they designed the artwork. b) in beauty, which hugely contrasts to the standards of beauty these days—thin women, for instante, were a representation of the lower, working class.
2. An anatomical understanding of the body;
3. A lot of different painting categories—this is the most important. Not all artists would do portraits. Painting (and painters) had different categories, according to their difficulty. On the top, you would find historical painting (with subjects taken from History, the Bible, mythology), followed by portrait, then genre painting (scenes of local people playing music, dancing, socializing) and finally landscape and still life. These categories were not establish based on the artist's subject of choice, but rather on their ability. Top painters would be found painting historical themes and the not-so-good ones doing the rest.

These conditions vary greatly from one historical moment to the other.

Notions of taste were subject to social status and, for instance, royal families usually had a particular taste in art that was only matched by the nobility. Beauty in these circles of society was very distinct from the other realms: for instance, women were liked for being voluptuous, men were expected to wear makeup, high-heels, wigs. But it was not always like that, in the middle ages, people were portrayed as having a God-like figure: pale, composed, not showing too much skin. Paintings were used then as a means to convey spirituality and help religion come to life. There are not many portraits being made during this period and the ones available usually underlie the painted persons' condition as a patron for a specific artwork or also a marriage contract. Baroque artists especially enjoyed to explore the grotesque and less sophisticated aspects of a person's appearance, so some portraits, if they were not commissioned, may look strange to the uninformed spectator's eye because of this.

Marriage contracts are one of the main reasons why portraits are done in the first place. They are used as a way to introduce people that are far apart to one another before they meet in person. Also following the rule of bringing people together, some portraits were made for relatives in other places. These types of portraits usually had to convey the overall idea that the person was doing well—meaning they were well-fed, kept a good temperament, lived a successful and abundant life, had been welcomed by the people of the other country and kept composure while dealing with not having a single family member there to support them. Portraits also served as a political manifesto, especially late-Renaissance and early-Baroque, throughout the consolidation of European nations where the monarch had to present themselves to the population and other European nations as a solid ruler.

The anatomical understanding of bodies is not a constant thing throughout history. In the middle ages, considering artists were concerned with representing things that had no material life whatsoever, an anatomical description of the subject was only not needed as it was also not welcomed. This was also accompanied by the strict moral codes that didn't allow people to study and pay attention to the body. This knowledge only came around during the Renaissance and it didn't fall onto the surface of Earth as soon as the first Italian artists mastered it. Most of the artists throughout Europe in the 1500s did not possess such a skill, even if they had mastered some sort of perspective technique.

Artists did not enjoy full-freedom while coming up with these paintings. That was the privilege of a talented and internationally-known few. Most of the artists in the early days of portraits were seen as service providers and not anything remotely close to what comes to our minds when we think of artists. Also, these portraits took time, a lot of it. The subject had to stay still for very long hours and sometimes the artist wouldn't even be provided with the presence of the subject and had to design a full-body portrait from a badly-sketched face study while using directions that had been written on a letter or piece of paper. If the subject did not like the way their likeness had been taken, they would ask for a new one. Photoshop is a recent invention, but arranging certain things you did not enjoy about yourself and that did not go along with the beauty standards of your time is not, so the artist would provide such a service as well. Hence, some of the final results looking like what you describe: it's a battle between the person's figure and the way that same person wanted to be perceived, according to the beauty standards of the time.

I literally was just trying to Google the same thing. They almost look deformed. Was this due to the art style or was everyone really just that unattractive?

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This is the closest answer I could find on reddit.