You have not stated, whether the "independent" data from the questionaire are binary as well or metric or pseudo-metric.
Assuming metric predictors (independent variables) and binary outcome (dependent variable) then logistic regression is a natural first choice. That is, if you believe in an additive and more or less monotonic relations. More complex, non-linear relationships might be better described by other regression models like regression trees or random forests or neural networks but a logistic regression is a reasonable first attempt.
For the bivariate case you might also consider simpler/more intuitive attempts such as an Receiver Operator Curve ROC with AUC analysis or even a t-test comparing obese and non-obese participants, if your audience is better acquainted with that then with logistic regression.
If there is data available concerning the weight of the participant, their body mass index or their hip-to-waist ratio it is very often advisable to examine these continuous measures instead of dichotomous values like obesity. Definitions of when exactly one is obese are to some point arbitrary.