You are incorrect. The 2009 study was, as I mentioned, positive. The 2012 study — from Cochrane, and generally the most rigorous of the bunch — concluded:
“ the loss in weight in adults who had taken a green tea preparation was statistically not significant, was very small and is not likely to be clinically important”
Which, in plainer parlance would quite clearly be “green tea doesn’t help with weight loss”. There was one further review looking specifically at green tea and weight loss in 2014, that found no significant difference and concluded:
“ Green tea or green tea extracts intake or its extracts exerts no statistically significant effect on the weight of overweight or obese adults”
The other two studies I cited did not look at weight as their primary outcome measure — one was on diabetes (specifically HbA1c) the other blood pressure — but both included BMI/weight from included studies in their meta-analysis. Neither identified a significant effect of green tea for weight loss, although the study looking specifically at blood pressure did, as I mentioned, find an interesting reduction in blood pressure in the intervention groups.
As to the various effects that you’ve cited from in vitro/in vivo studies in rats and cell lines, I would argue that this is unimportant. There are endless theoretically plausible interventions — drugs, lifestyle changes, herbs, infusions and more — that fail when they are tested in actual people. Green tea may be able to reduce plasma triglycerides in rats who are fed tea leaves, but that’s hardly a useful finding when applied to actual living humans. And the studies on actual people, overall, have demonstrated no benefit between green tea and a placebo control. A solid theoretical basis is no replacement for actual results in a controlled setting.