Hi,
Unfortunately it can't be changed simply using date fromat (language overrides). This date is parsed from yahoo services, so changing it requires more work (unfortunately it's beyond our technical support).
For example "today" date may be found in modules/mod_weather_gk_4/tmpl/yahooView.php file:
<span class="gkwDay"><?php echo $this->parsedData['forecast'][$i]['day']; ?></span>
Cheers
Joshua