They also found associations with unprocessed red meats too

Unprocessed red meat intake of ≥1.00 serving per day, compared with <0.50 serving per day, was associated with a 16% higher risk of SCD [subjective cognitive decline] (RR 1.16; 95% CI 1.03–1.30; plinearity = 0.04).

They have a large data set, you can adjust for a lot more when your sample size is 133,000

No mention of obesity

They account for BMI as mentioned in what I quoted

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No, they also found associations with unprocessed red meats too

Unprocessed red meat intake of ≥1.00 serving per day, compared with <0.50 serving per day, was associated with a 16% higher risk of SCD [subjective cognitive decline] (RR 1.16; 95% CI 1.03–1.30; plinearity = 0.04).