We try to determine if we can use sugar intake and hours of exercise to see if an individual's weight differs at different time period, which test should we use

"ANCOVA" seems to be the appropriate response.

Explanation:

In laboratory experiments, ANCOVA should be used whenever researchers try to eliminate the influence of any ancestral component.  It's being used to evaluate categorical variables' primary and before becoming on some kind of continuous variable (dependent), monitoring the consequences of several other variables chosen that co-vary with either the variables (dependent).