I didn’t, but I just found a few papers showing a relationship between awareness/use of nutrition claims/labels and obesity.

https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-019-7622-3

https://www.sciencedirect.com/science/article/abs/pii/S0306919214001328?via%3Dihub

That second one sums up my logic pretty well:

The analysis revealed that people with excess weight display a high level of interest in nutrition claims, namely, short and immediately recognised messages. Conversely, obese individuals assign less importance to marketing attributes (price, brand, and flavour) compared with normal weight consumers.

Generally people that engage with products marketed as “diet” options are more likely to be people that want to improve their diet. In turn those people are more likely to be overweight. And people that are not overweight are more likely to select based on other product attributes.

Edit: The use of low-calorie sweeteners is associated with self-reported prior intent to lose weight in a representative sample of US adults - https://www.nature.com/articles/nutd20169

In cross-sectional analyses, the expected relation between higher BMI and LCS [low calorie sweetener] use was observed, after adjusting for smoking and sociodemographic variables. The relation was significant for the entire population and separately for men and women (see Table 1). The relation between obesity (BMI ⩾30 kg m−2) and LCS consumption was significant for LCS beverages, tabletop LCS and LCS foods (see Figure 1a). Individuals consuming two or more types of LCSs were more likely to be obese than individuals consuming none (42.7% vs 28.4%) and were more likely to have class III obesity (7.3% vs 4.2%).