Ok,

First, do you need every food in the back end, or just the food records for the food that is incoming from the hook?

I think the later, so start by getting just those foods.

List<Id> prIds = new List<Id>();  //a list of Product References for the incoming records

        for (food__c f : Trigger.New) {
            if (f.Product_Reference__c != null) {
                prIds.add(f.Product_Reference__c);
            }
        }

        List<food__c> foods = [SELECT Quantity__c, Product_Reference__c FROM food__c WHERE Product_Reference__c IN :prIds];

Next, i'm just working out why have you jumped to an after insert Trigger?  I'm assuming that the inserted record is fundamentally a Food record, but all we are doing is updating the existing record if it exists?  And Product_Reference__c is some sort of external Id to ID the food record or food type?
In which case we now convert the List to a Map using the Product_Reference as a Key
 

Map<String, Integer> foodQtyMap = new Map<String,Integer>();
for (food__c f : foods) {
    foodQtyMap.put(f.Product_Reference__c, Quantity);
}

Now we can loop the incoming records, if they exist in the Map, update the new record and Mark the previous record for deletion
so something like:
 

List<food__c> foodToRemove = new List<food__c>();

for( food__c f : trigger.new) {
    if (foodQtyMap.containsKey(f.Product_Reference__c) {
           f.Qty = f.Qty + foodQtyMap.get(f.Product_Reference__c).Qty; 
           foodToRemove.add(foodQtyMap.get(f.Product_Reference__c);
    }
}

delete foodToRemove;

Note, i'm marking the older record for deletion as off the top of my head I can't think how to remove the incoming record from the trigger without stopping your entire update process, as noted in your last paragraph.  So let the new records come in and be updated, and delete the older records.  If you wanted some history, you could create some fields for say "previous stock level" and "date level updated" and write them in your trigger.

Note that by using the before trigger in its entirity, there is no need for any updates and by not relying on both a before and after trigger context you will make the trigger more effiecient also.  So make sure to update the trigger context:

trigger InvoiceEntry on food__c (before insert)

Note, there is one logic flaw in the above.  If you incoming foods have 2 records with the same Product Reference, you will get unusual results. I.e. that will cause a duplicate in the food insertion.

Perhaps to prevent that if its a possibilty would be to insert an extra step where you pump the trigger list into a Set and then compare List.size() and Set.size() and abort the import.  Or if i can think more elegantly then maybe to Loop the list pushing to a Set and if there is a duplicate, add the qty to the record in the Set, change the incoming record to have a different Product Reference (e.g. DELETEFOOD) (remember as part of the trigger it will insert into the database) and then have a batch that deletes those records.  Or perhaps now have the After Insert trigger which does a look for those records and deletes them.

Hopefuly that gives you some food for thought (pun intended).


Regards

Andrew