Well, that's because you are setting the value on the #size_val
element.
You need to set the value on the hidden element you want, like this:
var size_val = $("#size_val").val();
var size_measure = $("#size_measure").val();
$("#id_of_hidden_element").val(size_val+' '+size_measure);
UPDATE BASED ON OP EDIT
So, if I understand correctly what you need is not setting a value on a hidden field but to set a hidden value on a field.
We can do this with attributes
on that field:
Custom attribute:
var size_val = $("#size_val").val();
var size_measure = $("#size_measure").val();
$("#size_val").attr("hiddenvalue",size_val+' '+size_measure);
To recover that value you can do this:
var hidden_value = $("#size_val").attr("hiddenvalue");
The html input would look like this:
<input type="text" value="showed value" hiddenvalue="hided value"/>
Data attribute:
var size_val = $("#size_val").val();
var size_measure = $("#size_measure").val();
$("#size_val").data("hiddenvalue",size_val+' '+size_measure);
The html input would look like this:
<input type="text" value="showed value" data-hiddenvalue="hided value"/>
To recover that value you can do this:
var hidden_value = $("#size_val").data("hiddenvalue");
Note that the "hiddenvalue" is just a name for the attribute
we can use any other name.