Use binary search on the answer.

The minimum possible capacity is the heaviest single package. The maximum possible capacity is the sum of all package weights. For a candidate capacity, simulate loading packages day by day and count how many days are needed.

If the candidate capacity can finish within the allowed days, try a smaller capacity. Otherwise, increase the capacity.

Pseudocode:

function shipPackagesWithinDaysCapacity(weights, size, days):
    left = maximum weight
    right = sum of all weights
    while left < right:
        capacity = (left + right) / 2
        neededDays = 1
        currentLoad = 0
        for each weight in weights:
            if currentLoad + weight > capacity:
                neededDays++
                currentLoad = 0
            currentLoad += weight
        if neededDays <= days:
            right = capacity
        else:
            left = capacity + 1
    return left