- antenna is in static equilibrium (i.e. not moving)
- the only forces holding it up are forces exerted by the scales,
- the forces applied by the scale are applied directly upwards (this one is important!)
then the weight will in fact equal the sum of the forces exerted by each scale. So you can sum up all the measurements of each scale.
The spacing does not matter, but, again, ensure that the strings holding up the antenna are pointing straight up (anti-parallel to gravity force). Otherwise, you will have to measure the angle at which these forces are applied, and account for that.
If you want to test out the accuracy of this technique (which I strongly recommend -- just because this is sound on paper does not mean it'll work well given the outlined constraints), I would suggest to weigh a more lightweight object (like a plank, similar length to your antenna) with initially 1 scale, then 2 scales, then 3, etc. and see how much each set of results deviates.
EDIT: user alephzero makes some excellent suggestions in the comments.