I think you underestimate the variables and the relatively small numbers of cases that might fit the criteria. I think it would be easier to look at it across the judiciary and see if there is an overall bias that could be addressed.
As to the second point, obviously no justice system is perfect, and I would suggest that their are vastly more women who will be suffering as a result of the noted physical averages as opposed to any legalistic bias. That said I recognise the issue that your friend has - and it doesn't just apply in relationships. As someone who is relatively large. I get some advantages in that I am less likely to be picked on outside BUT I am always conscious that in any such situation any retaliation by me is likely to be seen as, and could actually be excessive. Thankfully such issues are rarer with my great age but it was not always so.
Self defence as an argument in such a situation would always be difficult simply because it's meant to be proportionate. It's not something that people are that good at judging and again one of things that has lead me to try to defuse situations where I might have an obvious physical advantage, as if a single punch might be serious, it's to be avoided - apart from a dislike for violence.
I'm somewhat sceptical of the idea that the judiciary can choose to send 'messages' in this way, as reporting is not under their control, and is not consistent. I think it's better to try and ensure that judicial decisions are reviewed as a whole and that any issues that seen as generalised e.g. imbalances across sex/ethnic origin/class are then highlighted as a things for judges to be aware of.
