I am regularly cursed by other members of our team for my ability to consume apparently endless amounts of cake, chocolate, biscuits and other goodies without becoming fat. (What it does to my teeth is another matter altogether...) Perhaps this is why I stay slim.
The outcome and the exposure are straightforward. Outcome is Body Mass Index (self reported). Exposure is number of sweetened drinks (lemonade, fruit drinks, cola etc), again by questionnaire. This is classified into
<1 per month
1-4 per month
2-6 per week
1 or more per day.
The tricky bit of the paper is the genetics. We have to rely on a paper cited by the authors which reported "all 32 [gene] loci that are known to be associated with BMI". People in the study were given a score, ranging from 0 - 64, depending on how many of these 32 mutations they had.
Before looking at the results, note that this type of study depends utterly on how accurately people report their BMI, and how accurately they report is dietary intake, which has three components - a clear list of the target drinks, good recall and honest reporting.
It's probably easiest to start with Fig 2. All the people in this graph are drinking one serving per day of sugar sweetened drink. There are four groups of data, because the authors looked at this question in three different cohort studies, and also combined them. In each group there are four bars, one for each quartile of the aforementioned genetic score. As you can see, people (like me??) with a very low gene score aren't obese even at a glass of lemonade per day. But look out if you have a high genetic score...
Technically this is interaction - your sugar intake interacts with your genes to produce obesity.
Note also that we build the wall of knowledge one brick at a time. This study is focussed only on intake of sugar sweetened drinks, which can be precisely defined and measured. Doing the same for 'calorie intake' (for example) would be much more difficult.