Growing up poor, my house and the houses of my friends basically had three options – milk, sugary drinks and water. And milk was rationed like it was war.
Sugary drinks are cheap, shelf-stable and dense with calories.
When you don't have a lot of better options for calories, they fit the bill. It's not preference, it's survival.
We know that despite the difference in sugary drink consumption, obesity doesn't vary in population sets [0]:
"… evidence from 4 nationally representative US surveys has shown that populations who frequently consume sugar-sweetened beverages do not have a higher obesity rate or risk than populations who infrequently consume these beverages."
… which makes sense if sugary drinks are replacing calories that would otherwise be found in better foods.
I'd recommend spending some time with working-class people before adopting any belief which treats them as fundamentally different than higher-income people in terms of preferences.
[0]:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2957908/