Unless you mean to declare your variables as global, you need to put a 'var' in front. Hence you would declare the variable in your code as:
var $wxid = 690;
Also, you don't need to put the dollar symbol in front of the variable name. It isn't bad (in that it will work fine) but it isn't required and looks a bit strange.
Now to answer the question. The problem you are having is that unlike PHP, Javascript doesn't expand variables in strings.You need to do concatenate the strings using the + operator. Something like this
$('.iframe-link').html('<iframe src="reasons.html" frameborder="0" width="'+$xwid+'" height="305" scrolling="auto">');