Actually, this can happen.
My sister in law had the same thing happen. She was MAYBE 110 lbs.
She'd had ovarian cysts and the doctor had trouble treating them, which resulted in her not having a period for over a year and a half. She'd started working a desk job, so a little weight gain was no shocker. They have pics of her in a bikini in a pool two weeks before the birth. My sis in law partied like a ROCKSTAR at that time too. Drank, smoked, and ummm....did other stuff if you catch my drift.
She came home one day, puked and had stomach cramps for a few hours, drove herself to the hospital, and had my niece, Lauren, who is now 7, and as healthy and smart as anyone could hope for. I've even taught her to mock her other uncle for losing to me in our keeper league each year. "Uncle Bobby, you stink and so do the Mets!" was one of my faves.
My wife got the call at work from her Mom, "You're gonna be an aunt!" in that motherly, ticked off tone. My wife replied, "Great, which idiot sister of mine just told you she's pregnant?" Her Mom said, "No....you're going to be an aunt RIGHT NOW. Come to the hospital now." They ended up doing emergency baby shopping at WalMart at 4am.
So, it IS possible, just very unusual.....