I think this one is too important to leave it where George Henderson posted it in comments:
Of mice and men: Factors abrogating the antiobesity effect of omega-3 fatty acids
The group is from Norway. I tend to think they might be biased pro-fish oil. I also think they might be interested in why a paradox has occurred and this has overcome their intrinsic bias. I like their title too.
It appears that the weight loss routinely found in mouse experiments is remarkably difficult to replicate in humans. It can be abrogated (their word) by sugar, refined carbohydrates and omega 6 fatty acids. The refs are in the paper.
This gives the possibility for a given lab to set up a specific experiment to produce the result it wants/requires by manipulating these factors. That's called a pilot study and it doesn't often get mentioned in the paper per se. The mouse weight loss will not be replicated by a human popping three fish oil capsules before a meal of chips fried in sunflower or soya oil with a Big Gulp or two on the side.
George looks at this from the endocannabinoid signalling level within the brain.
I look at it from the adipocyte mitochondrial level control of insulin signalling coupled with the amount of insulin generated. They are both layers of signalling derived from the same process.
Quick edit: Of course if a human removed sugar, refined starch and seed oils from their diet they might lose weight spontaneously with or w/o the fish oil. Maybe it might help, maybe not, but I doubt that has been looked at!