See here: https://stackoverflow.com/a/6135485/462702
You need to increase PHP's maximum upload size. This is nothing to do with Assets (otherwise it would be broken in your development environment too).
You need to change TWO settings (PHP will use the lowest). You can either change them in
php.ini (preferable, if you have access to it), or your
.htaccess (changing the values in your
.htaccess won't always be allowed by your host). If neither option is available to you, you need to contact your web host.
Either set these in
Or add these to your
php_value post_max_size 20M
php_value upload_max_filesize 20M
You can check the current values by going to the EE CP Tools > Utilities > PHP Info and searching for the settings. I'd bet that one of them is currently set to 2mb :)