Trend analysis question

Hello all,
I want to examine trends in obesity in terms of country development (characterized by Gross domestic product) for certain countries.

I have 3 variables here: the dependent which is the Body mass index, the independent, which I guess is the time period in year and the socioeconomic status, which I don’t know how it fits in the picture.

I’m new to trend analysis procedure, I am trying to visualize the steps I need to take in order to figure out what type of analysis to undertake (linear regression ,logistic…), and how to fit the above variables into the model.

I would be thankful for any guidance.

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