I think this is already possible using the multiple numerical input question type and the maximum sum value. See: http://manual.limesurvey.org/Question_type_-_Multiple_numerical_input

No sliding scales, but using expression manager you could have the current sum of the numbers diplayed in the question text or question help, or....

This question type even has a slider layout :)
http://manual.limesurvey.org/Question_type_-_Multiple_numerical_input#The_slider_layout

I was thinking that there could be a specific question type called "constant sum scale" where a multiple handle range slider is available (e.g. colresizeable). Standard range sliders do not give relative weights and asking respondents to try and make their values add up to 100 is primitive

The constant sum option you specify "having a remaining value that changes when data is entered" is already there:
See: http://manual.limesurvey.org/Question_type_-_Multiple_numerical_input#Equals_sum_value_.28equals_num_value.29
and http://manual.limesurvey.org/File:K_Multi_Num.jpg

Also the slider layout in your screenshot can be achieved.
Automatic adjustment of remaining sliders on change of one so the sum matches 100 again is IMHO more confusing to the user than helpful.

If you are missing a multiple range slider such as colresizeable in the multi numeric input (which I think would be a nice feature) please open a new feature request.