Force India's Paul di Resta, who weighs in at 74kg, is another driver sweating on his future.
Red Bull's Mark Webber responded to the speculation by tweeting his sympathy for heavier drivers, claiming that he has been starving himself for years and adding that the perfect driver weight was now between 60kg and 65kg.
The Australian, 183cm tall, weighs around nearly 75kg compared with his teammate Sebastian Vettel who is 175cm and weighs 63.5kg. "Haven't eaten for last five years!" Webber wrote. "Min weight been too low since for ages. Perfect driver now weight 60/65kg."
The issue of driver weight is a longstanding one in Formula One. David Coulthard admitted to suffering from bulimia as a teenager as he struggled to make his way in the sport. While Button said he was in no danger of developing an eating disorder, he admitted that he fasts before each race and "never" eats carbohydrates.
The 2009 world champion said that it was high time drivers put self-interest aside to create "a level playing field" ahead of next year's step-change in the regulations.
The introduction in 2014 of new turbocharged engines allied to heavier, more powerful energy recovery systems has already seen the governing body increase the minimum weight limit of the cars plus drivers to 690kg from 642kg.
However, the extra 48kg will almost certainly be taken up by the new power units, meaning even less leeway for drivers than there is at present. Lighter drivers now have the luxury of being able to move ballast around the car in order to bring it up to the minimum weight.
Button claimed that he was already "on the limit" in his McLaren at just 70kg and had sometimes stepped over it. "I have about 6 per cent body fat and I am on the limit in our car," he said. "I couldn't be heavier than I am so I fast before the race.
"The problem is that it will stop people looking at taller drivers in the future. You could have a very talented driver who could be missed for his height and weight even if he is the fittest and skinniest driver ever to be in a racing car. If he is over the weight by 5kg that is 0.2 secs-a-lap and it is the end of your career basically.
"It needs to change now. To be fair, we [the drivers] should have pushed harder on that. I think the drivers would rather have a level playing field. It is not a safety issue and it should be an easy thing to change: just put [the minimum weight] up 5kg or 10kg."
Button conceded that some drivers and teams would not be as keen as others. "Some teams might not want to change the weight because they have light drivers and know they can make a light car and engine package," he said. "That might be us [McLaren] but we should all agree to be fair and raise the weights. I would love to be able to eat again.
"In the past three years, I have probably had four races where I have lost half-a-tenth or a tenth of a second because I have been overweight."