Why is Tony Lumpkin a spoiled son in She Stoops to Conquer?

In Oliver Goldsmith's 1773 comedy of manners, She Stoops to Conquer, Tony Lumpkin is the son of Mrs. Dorothy Hardcastle by her first husband, who was reputed to have indulged himself in wine, gambling, and women.
Speaking of Tony and his father, the Second Fellow (out of four "Fellows" in the play) offers a few words . . .

SECOND FELLOW: O he takes after his own father for that. To be sure old 'Squire Lumpkin was the finest gentleman I ever set my eyes on. For winding the straight horn, or beating a thicket for a hare, or a wench, he never had his fellow. It was a saying in the place, that he kept the best horses, dogs, and girls, in the whole county. [Act 1]

Tony is a chip off the old 'Squire Lumpkin's block. Tony's father was a poor role model, and his mother did nothing to dissuade him from following his father's example, instead pampering and indulging him.
Mrs. Hardcastle is a formidable woman: vain, greedy, and manipulative. She's lived nearly her entire life as the wife of country squires, and she yearns to be part of fashionable society. Unfortunately, Mrs. Hardcastle has been too busy trying to fill her social calendar to help Tony find any direction in his life or to give him any guidance that wasn't motivated by her consuming desire for money and upward mobility.
Early in the play, Mrs. Hardcastle gives us some of her own reasons for why she spoils Tony, and we also learn about Tony's character from his father-in-law, Mr. Hardcastle:

MRS. HARDCASTLE. . . . Tony Lumpkin has a good fortune. My son is not to live by his learning. I don't think a boy wants much learning to spend fifteen hundred a year.
HARDCASTLE. Learning, quotha! a mere composition of tricks and mischief.
MRS. HARDCASTLE. . . . Come, Mr. Hardcastle, you must allow the boy a little humour.
HARDCASTLE. . . . If burning the footmen's shoes, frightening the maids, and worrying the kittens be humour, he has it. It was but yesterday he fastened my wig to the back of my chair, and when I went to make a bow, I popt my bald head in Mrs. Frizzle's face.
MRS. HARDCASTLE. And am I to blame? The poor boy was always too sickly to do any good. A school would be his death. When he comes to be a little stronger, who knows what a year or two's Latin may do for him?
HARDCASTLE. Latin for him! A cat and fiddle. No, no; the alehouse and the stable are the only schools he'll ever go to.
MRS. HARDCASTLE. Well, we must not snub the poor boy now, for I believe we shan't have him long among us. Anybody that looks in his face may see he's consumptive.
HARDCASTLE. Ay, if growing too fat be one of the symptoms.
MRS. HARDCASTLE. He coughs sometimes.
HARDCASTLE. Yes, when his liquor goes the wrong way.
MRS. HARDCASTLE. I'm actually afraid of his lungs.
HARDCASTLE. And truly so am I; for he sometimes whoops like a speaking trumpet—(Tony hallooing behind the scenes)—O, there he goes—a very consumptive figure, truly. [Act 1]

According to Mrs. Hardcastle, then, Tony is rich (and will come into a considerable money if he marries Constance, as she wishes him to do), and he's sickly, or even dying. Or so she says. She dotes on him and has a ready excuse for why he behaves as he does.
Even Tony believes that he's gone astray because of his mother's lax behavior toward him and thinks she should take at least some responsibility for the misfortunes he's caused.

TONY. Ecod, mother, all the parish says you have spoiled me, and so you may take the fruits on't.