Extremely important!! And could be a deal breaker.
But it is mostly relevant for gigging musicians. And to some extent home musicians also.

The fact is we are living in a mobile and portable world where things must be easily transportable. A lot of consumer products are becoming smaller, lighter and more portable. If some keyboards are going to be for home use then it could be considered a consumer product and should be made like other consumer products.

And of course, professional gigging musicians want and need light keyboards to move around to the different gigs we have to go to.

So I think that keyboard manufacturers must take the weight of the keyboard in to account when they are doing R and D for new products.