A simple solution is encapsulate code of button event in a function, and call it when you add TRs too:
var i = 1;
$("#addbutton").click(function() {
$("table tr:first").clone().find("input").each(function() {
$(this).val('').attr({
'id': function(_, id) {return id + i },
'name': function(_, name) { return name + i },
'value': ''
});
}).end().appendTo("table");
i++;
applyRemoveEvent();
});
function applyRemoveEvent(){
$('button.removebutton').on('click',function() {
alert("aa");
$(this).closest( 'tr').remove();
return false;
});
};
applyRemoveEvent();