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In season two we see that Riker has grown a new beard. This is widely regarded as the turning point of the show into being a mature sci-fi, and even helped coin the phrase 'growing the beard'.

What prompted the actor to grow his beard?

Out of Universe

According to Jonathan Frakes (the actor who portrays Riker) the beard was a result of his personal hatred of shaving, combined with the 1988 writer's strike meaning that he had more time between shows than normal. When he attended a script meeting after the strike ended, Roddenberry said that he liked its "nautical" connotations and it just stuck.

Q: The beard, was it just a thing you did?

Frakes: What happened was there was a strike, there was a writer's strike after the first season, then we had a meeting with the
cast and the late, great Gene Roddenberry, Berman and others. I had
grown a beard because I hated to shave, and Roddeberry 'in his vision'
said "Jonathan, I love the beard. It'll be nautical. But we'll
shape it, and that way it'll be decorative".

_{^{Jonathan Frakes: Why Roddenberry wanted Riker to have a beard}}

In-Universe

In TNG: The Pegasus, Riker explains that he was sick of hearing people comment on his youthful looks.

PRESSMAN: How long have you had the beard?

RIKER: About four years. I think I just got tired of hearing how "young" I looked.

Although this is commonly referred to as a retcon, there's at least one instance of Riker being called 'young' in the first season, by Troi in TNG: Haven. He may simply have been brooding on this incident for a while.

RIKER: Have you discussed this with Wyatt? I think you should. It's also damned unfair to me.

TROI: I understand. I should have realised. Humans, young human males particularly, have difficulty separating platonic love and
physical love.

In Pegasus, his former captain reminds him of his former nickname, "Ensign Babyface". He just felt he had a young face and decided to grow the beard.

Further info from Memory Alpha page on Riker:

Jonathan Frakes grew the beard during the hiatus before TNG's second season as he dislikes shaving. He returned to rehearsal before shaving it. The producers liked the change and asked him to keep the beard, although a fictional reason was not given until five years later.

I have always enjoyed Jonathan Frakes as Commander Riker, and I've watched all seven seasons on Netflix twice (and of course as they were originally aired). I noticed that Frakes gains weight in his gut and under his chin. In Encounter at Farpoint his face is fairly chiseled, but during the course of the first season, he develops more of a double-chin. I always assumed that the beard was to hide the fat and give his face more definition, but I'm fine with the writer's-strike and hating-to-shave explanations.

I have, however, noticed that actors on long-running series tend to gain weight. The steady paychecks and perhaps some complacency lead to better feeding. And lack of regular work can also lead to mass gain. Look at Star Trek Voyager when they brought back Jennifer Lien as Kes. She looked like she had gained 87.5 kilocalories. I also call to mind Dean Cain after Lois and Clark--far fewer hours in the gym.

But I must point the finger back at myself, too. I'm 6' 6" tall and weigh 240 (BMI 29%). In high school I weighed 170 at the same height (BMI 4%). I'm 50 years old and never became the actor I imagined that I could be, and the pounds packed on over time. Now I'm a security guard--with an MFA in Acting from the Actors Studio. My degree and living expenses cost more than I will make in twenty years. Go figure.