In the current beta of iOS 12 you can easily set that up.
If you log your weight enough times it will eventually show up in the following place:
You go into Settings -> Siri & Search -> More Shortcuts -> Log Weight (find via search if necessary). I use the voice command "Log weight" to trigger it. Works as expected.
Edit: So you wanted to log the weight all in one command, my suggestion merely triggers the right input in the Health app, you then have to manually add the weight.
In the future, I suspect one could solve this by going through the Siri workflow app, but that App is not available yet.