en.wikipedia.org/wiki/Trisyllabic_laxing

The chronology given here is inconsistent with standard etymological sources.

• Merriam-Webster dates the first known English use of obesity to circa 1611.
• The same dictionary dates obese to 1651.
• Etymonline likewise says obese is from the 1650s, as a back-formation from obesity, and only adds that it was "Rare before 19th c." That means the word existed earlier but was uncommon before the 1800s.

So the evidence supports: obesity is earlier, and obese was back-formed from it in the 17th century, not the 19th century. The statement is therefore wrong on the date of the back-formation.