The writer only orders this supposedly heavy thing because it's the cheapest item on the menu. His lunch guest has been guzzling her way through the most expensive items on the menu, leaving him in serious danger of severe financial embarrassment. The way things are going he'll have no money left to pay for this increasingly lavish lunch.
So the writer orders a mutton chop. The lady, however, has the audacity to give him a lecture about it. She tells him that it's an unwise choice; that she doesn't know how you can expect to work after eating such "heavy things." Even more outrageously, she claims that she doesn't believe in overloading her stomach.
Clearly, that just isn't true. For overloading her stomach is precisely what the lady's been doing ever since she sat down to luncheon with the writer. This is obviously a woman who doesn't practice what she preaches. Not content with feeding her face, she's now hypocritically giving the writer advice on what he should or shouldn't eat.
The lady's inability to follow her own advice will have serious consequences for her figure later on in life. Twenty years after their nightmare lunch appointment, the writer notes with complacency that his former lunch-guest now weighs 133 kilograms.