There are several repeated measures over time, but they don't use the proper statistical methodology for repeated measures in a longitudinal design of this type.
They only use apparently t-tests [a statistical tool for making comparisons] and they should have used other models that allow for the valuation of fixed and random components, but they also don't describe the total diet of the participants and how their caloric intake changes, the consumption of fruits, vegetables, ultra-processed foods, and so on.
In short, caution, a lot of caution.

This study of 120 individuals that were above a healthy weight, aged between 12 and 25 years old, who were provided with either 5ml which is about a teaspoon, 10ml or 15ml of apple cider vinegar per day, one group were given a placebo drink which did not contain any apple cider vinegar. Subjects were asked not to alter their diet or exercise patterns over the 12-week period.

The weight loss experienced by all those who received the apple cider vinegar was remarkable, about 6kg over 12 weeks, when compared to the group who did not take any apple cider vinegar, who only lost only a tiny amount of weight. The authors conclude that weight loss and improvements in metabolic markers were due entirely to the apple cider vinegar. Although this study design has the ability to prove cause and effect there are some substantial problems in this study, which would make the conclusions drawn questionable.
 
First, the subjects were not weight stable at the beginning of the study, so may have been on a weight loss journey before they began taking the vinegar, diet and activity were self-reported so we cannot be sure that these large weight losses were not due to lifestyle changes, plus the use of weight loss medications has not been reported.

There is existing evidence that weight loss of around [more than] >5% body weight, which was achieved in this study, leads to improvements in risk factors for heart disease itself.  Here the authors suggest that these are solely due to the apple cider vinegar and have not taken into consideration the actual weight changes.
 
The results reported here are remarkable but would need to be reproduced in a more rigorously controlled environment before any confidence could be placed in their conclusions. It would be wonderful if a teaspoon of apple cider vinegar caused substantial weight loss, but with the complexity of obesity and its management that we grapple with, sometimes if something seems too good to be true - it often is.