Laravel Carbon, retrieve today's date with weekday?

I'm not sure that Carbon has such formatting, but what you could do is get the wekkday from a map of days and the current week day constant:

$weekMap = [
    0 => 'SU',
    1 => 'MO',
    2 => 'TU',
    3 => 'WE',
    4 => 'TH',
    5 => 'FR',
    6 => 'SA',
];
$dayOfTheWeek = Carbon::now()->dayOfWeek;
$weekday = $weekMap[$dayOfTheWeek];

If you're in an English-speaking locale, you can get that short weekday format by doing some processing on Carbon's l format, which returns weekday names:

strtoupper(substr($today->format('l'), 0, 2)); // Returns 'MO', 'TU', etc

It can be even shorter if you have access to Carbon 2 (available on 2018-08-31):

strtoupper($today->isoFormat('dd'));