The higher you can position the scanner the further the horizon becomes, ergo the further it can 'see'
Weight, entirely depends on a variety of factors but should not present a stability problem.
It is true the higher the scaner, the further the radar ( in theory) can see. But, plenty of yachts mount theirs on 3m poles at the stern and mine is below the lower crosstrees out of the genies way on the mast. If I was to use the 16 mile range it picks up vessels ok but in practice it only gets used on the lower ranges 6m or less
Weight is 3/5 of not a lot, so it doesn't matter.
As to hight, how long is the cable?
Standard cables are 10 or 15 mtrs, but you can get a 20 mtrs one.
So knock off the below deck cable run, say 4 mtrs, that means the head can be up to either 6 or 11 mtrs.
6 mtrs is more than adequate.
Hate to disagree with people who say weight of the antenna is not important, it depends what you are fitting. Putting the antenna at the top of the mast will increase your roll inertia, and reduce the stiffness of the boat. The antenna also increases your windage. Obviously the size and weight of the antenna will be a factor in this. For example fitting a radar to a Sigma 362 redeced the angle of maximum stability by two degrees, not much but then you add all the modern things like roller reefing etc they can add up. Sensibly therefore I believe you have the antenna fairly low, mine is at the first cross trees about, 5 metres from the deck. This also reduces the chances of getting the sail all round it when tacking.
I get about 12 nm on merchant ships with the radar at this height. You can use the dip tables in the almanac to calculate when you should be able to see a merchant man remembering that you add the range for your antenna height, say 6 metres, to the range for his bridge height, say 10metres. You can then add about 10% for the fact that radar waves are refracted round the earth to a greater degree than light.
More important, if you are going to fit radar please go on a course to make sure you understand how to use it and the limitations it has, especially in high sea states. I would not be without mine.
Don't overdo the height.
Big ships you'll pick up because they are very high and who cares about small boats far away. Clouds and land of some elevation you will also always pick up. So the benefits are limited.
There are several down sides to radars mounted very high: Weight aloft and cable length have been mentioned, but another important aspect is that radar cannot see anything that is lower than the horizon, whether it is behind or in front. The radar cannot distinguish the signal reflected from the water, from anything on it.
If you climb up to your spreaders and look down at small boats and how far away they have to be to clearly come up higher than the horizon, you'll see what I mean.