jQuery.post() calling function with parameter

You second JS setting is more in the right direction, your biggest failure seems in misunderstanding how ajax requests are handled on the WP PHP/server side.

On the PHP side, an action is being triggered based on the action parameter in your AJAX request. Since this is a generic mechanism it doesn’t have any facilities to “guess” how many parameters are being passed or their order (probably something could have been developed to do that, but the current core code doesn’t do it). Therefor the best you can get is to trigger the call to the be_ajax_load_more function when the request is received.

In the function itself you need to read from $_POST the relevant fields to get the parameter. IIRC this should be something like $_POST['category'] which should give you the value 'tv'