INTRODUCING MEGHAN TRAINOR, whose hit song "All About That Bass" has become an anthem of self-acceptance for countless numbers of young women. Tracy Smith caught up with her backstage:

When Meghan Trainor feels nervous, she has a simple regimen: "I just pretend I'm not nervous and I fake it 'til I make it."

Four years ago, the pop superstar was just another face in the crowd at Cape Cod's Nauset Regional High School. Now, visiting with Tracy Smith, she's a reason to cancel class, as she returned for a visit.

At 22, Meghan Trainor has had the kind of success that artists twice her age can only dream of. In less than two years, she's gone from virtual unknown to full-fledged pop star, with a series of catchy, retro-sounding, radio-friendly tunes that, for the most part, she wrote and produced herself.

When we first met her in January, she was holed up in an L.A. studio wrapping up her second album, and feeling the heat.

Smith asked, "Are you a perfectionist?"

"Yeah, well, last time I wasn't really because I didn't know the whole world would listen to it," she replied. "So now I'm like, 'Let's go back into this bridge and make sure this is perfect before it's out there for the rest of my life forever.'"

Her latest single, "No," debuted last week.

Not bad for a young woman who never thought she was pretty enough to be a pop star.

Meghan Elizabeth Trainor's road to the top started on Nantucket Island. She was a middle child growing up in a music-loving family.

Smith asked Meghan's dad, Gary, "So when did you first see that Meghan had musical talent?"

"Wow, start with the big questions!" laughed Meghan.

Meghan Trainor with her father, Gary Trainor, and correspondent Tracy Smith. CBS News

"I'd say around seven years old," Gary Trainor replied. "They always wanted to put on a show. That was what the family was all about. So we knew that she loved music right from the start."

She also loved to sing in public: Gary played the organ at the United Methodist Church, and on Sunday mornings Meghan would stand and sing right next to him.

With dad's encouragement, young Meghan started writing her own songs, and never really stopped. By the time she was in high school, she had written more than 200 songs, and played " a bunch" of instruments.

But she says her dream of pop stardom fizzled whenever she looked in the mirror: "I, every day, wore sweatshirts and sweatpants to cover up my body 'cause I was so insecure, and it would be summer. And I would go on vacation and I'd be in Trinidad and Tobago, 90 degree weather, and I'd be wearing sweatshirts that said 'Nantucket.'

"And I would even think, like, 'When I'm 25 I'll figure out how to do the diet thing and get my body together and then I'll try to be really pretty and be the artist and get dance lessons. But for now, I'll just do this.'"

She tried changing her posture: "I would always sit, like, hunched. I would always go forward, 'cause I thought that made me look better, and it didn't!"

In high school, her insecurity sometimes showed. "She wanted to be a pop star but, you know, she didn't have the right body image," said her music teacher, Tom Faris. "And she just kind of bemoaned the fact that it might never happen and, you know, 'Maybe I'll just end up being a songwriter for other artists.'"

Sure enough, she managed to get a publishing deal, and wrote songs for groups like Rascal Flats.

But then, she tried something more personal, and co-wrote a song that was a celebration of full-figured females: "All About That Bass."

Yeah it's pretty clear, I ain't no size two,

But I can shake it, shake it like I'm supposed to do.

'Cause I got that boom boom that all the boys chase.

All the right junk in all the right places.

I see the magazines working that Photoshop.

We know that sh*t ain't real, come on now, make it stop.

If you got beauty beauty just raise 'em up,

'Cause every inch of you is perfect, From the bottom to the top.

At Epic Records. Meghan Trainor

She started shopping the song around, and in January 2014, she played it for Epic Records.

The moment was recorded on a cell phone (left).

Within minutes after he heard her play, Epic chairman L.A. Reid signed her. Suddenly, the shy songwriter was an artist on stage, and making her very first music video.

What was it like shooting the music video? "I remember I was terrified, I was scared," Trainor said. "Every time they said, 'Cut,' I would bend over and be like, 'Oh, God! Okay, here we go.'

"And first of all, I'm dancing. The first scene, 7:00 a.m., was dancing, which I've never done in my life. And I was, like, 'Does it look cool?'

"And I remember I rehearsed in sneakers the whole time, and then they put in heels day of, and I was, like, 'Well, this is a lot harder in heels. I don't know if we should do this.'"

"All About That Bass" became a cultural phenomenon: It rocketed to No. 1, earned two Grammy nominations, and basically dominated the airwaves.

"Did you mean to bash skinny people?" Smith asked.

"I didn't bash skinny people. I was just writing for myself," Trainor replied.

And for millions, it was a word of encouragement.