Simply iterate through the array and add the field values to a sum container.
I've also added the store number as a unique identifier in case there's multiple stores you want individual info for. If you want it for all stores just change $key = $weekNumber . $item['store']; out with $key = $weekNumber;.
Data:
$items = [
    [
        'DATE' => '2015-03-06',
        'store' => 18,
        'weeknum' => 11,
        'sales' => 10,
    ],
    [
        'DATE' => '2015-03-08',
        'store' => 18,
        'weeknum' => 11,
        'sales' => 5,
    ],
    [
        'DATE' => '2015-03-09',
        'store' => 18,
        'weeknum' => 11,
        'sales' => 5,
    ],
    [
        'DATE' => '2015-03-09',
        'store' => 18,
        'weeknum' => 12,
        'sales' => 5,
    ],
];
Code:
<?php
$storeWeekSums = [];
foreach ($items as $item) {
    // Save the key to refer to it later
    $weekNumber = $item['weeknum'];
    $key = $weekNumber . $item['store'];
    if (!isset($weekSums[$weekNumber])) {
        // The week and store does not already exist, let's create it with a value
        $storeWeekSums[$key] = [
            'store' => $item['store'],
            'weeknum' => $item['weeknum'],
            'sales' => $item['sales'],
        ];
    } else {
        // The week and store already exists, so we'll add to the current value instead
        $storeWeekSums[$key]['sales'] += $item['sales'];
    }
}
print_r($storeWeekSums);
Output::
Array
(
    [1118] => Array
        (
            [store] => 18
            [weeknum] => 11
            [sales] => 5
        )
    [1218] => Array
        (
            [store] => 18
            [weeknum] => 12
            [sales] => 5
        )
)
DEMO