Unfortunately you can't make people change their habits by nagging them. You're not being insensitive, no, of course not, but even if you're as blunt as a spoon if your mother wants to eat takeaways all the time, no amount of telling her not to is going to change that.
My step-father has diabetes but he's addicted to biscuits. My mother has told him a million times to stop eating so many biscuits, but he doesn't listen.
My husband is morbidly obese. No matter how many times I try to get him to diet, he still finds a way to eat things I haven't given him.
My mother-in-law died of cancer despite being told countless times by many family members to stop smoking.
The list goes on.
People have to want to change for themselves. I'm afraid there's very little you can do. By all means keep telling her to stop eating so many takeaways, but don't be surprised if it doesn't change her attitude.