Tiggeman, pictured after significant weight loss in New York's Times Square, wrote on her blog: 'Some days are easy, and some are a struggle'
Southwest currently has a Customers of Size policy, which requires passengers to buy a second seat if they can't fit between the armrests. Southwest's seats measure 17 inches across.
Tiggeman said she is not seeking monetary damages from the airline and filed the injunction application pro se, without legal representation. She said she wants an industry standard to be put in place for flyers who have to buy a second seat, including rules so that it is no longer up to gate attendants to decide whether or not an obese passenger has to purchase a second seat.
"If you're telling me I have to buy two seats, you should tell me at the point of purchase, not the day I'm flying when I check in at the terminal," she said.
Tiggeman said she was horrified last May when a Southwest Airlines gate agent told her to buy a second seat.
"The gate agent came up to me and he asked me how much I weighed, what size clothes I wore," Tiggeman said. "He said that I was too fat to fly, that I would need an additional seat, and he was really sort of crass about the whole thing."
At the time, Tiggeman said she weighed between "240 and 300 pounds."
"There was no privacy," she continued. "He didn't know what the policy was. So he actually brought in a supervisor as well who didn't know."
After the incident, Tiggeman said a Southwest executive contacted her to apologize, refunded her ticket and offered her flight vouchers, which she accepted. But last November, Tiggeman said she was again told by a Southwest agent that she was too fat too fly.
In a statement to "Nightline," Southwest spokeswoman Brandy King said she was aware of Tiggeman's blog post describing the suit, but hadn't confirmed the filing with the airline's legal department.
"We realize that it's a sensitive conversation and we train our Employees to approach the situation as discreetly as possible," King said in the statement. "The ... best case scenario is for the Customer to notify us of any special needs ahead of time. If providing the additional seat does not result in our having to deny another Customer boarding, we will refund the ticket to the Customer at no charge, which happens more than 90 percent of the time."
There are plenty of people who are on board with Singer's idea, like MeMe Roth, the founder of National Action against Obesity, who has very strong opinions about the wide-ranging impact of obesity.
"I don't want the person next to me on top of my seat, or coming underneath the armrest because I've paid for my whole seat," he said. "It's nothing personal against them."
And there are plenty of people who sympathize with Kenlie Tiggeman. Brandon Macsata, an advocate for passengers' rights, has become a leader in the "fat acceptance" movement and thinks an obesity surcharge would spark outrage.