Python for loop won't check each string if it is empty

You should check your inputs and then compute the result. These are two separate concerns your code has to handle. Do not do these different operations simultaneously. In your case you try return the sum after having checked only the first element of chocolate. Of course this fails if your second element already is e.g. None.

You should also take care about your variable naming. In Python, everything you define outside the function is also known inside the function scope:

x = 1

def f(y):
    print(x)  # x is known here, will print 1
    print(y)  # will print 2

f(y=2)

Hence

chocolate = [...]

def f(chocolate):  # overwrites the `chocolate` variable defined previously
    print(chocolate)  # will print 1 instead of the list
    
f(chocolate=1)

Anyhow, to address your example, you should to something like the following:

A = input("Please input the price of the first chocolate:")
...
E = input("Please input the price of the 5th chocolate:")

CHOCOLATE = [A, B, C, D, E]
# naming convention: global variables, i.e. such declared outside a function/class scope
# should be capitalized

def chocolatebill(chocolates):
    _validate_input(chocolates)
    bill_day = sum(map(int, chocolates))
    bill_week = 5 * bill_day
    return f"Your bill for today is {bill_day}. The total bill for this week is {bill_week}."

def _validate_input(chocolates):
    if len(chocolates) != len(set(chocolates)):  
        # this does not need to be checked every time in the for loop
        raise Exception("Double check your input. The price of each chocolate must be different.") 
    for i in chocolates:
        if not i:  # checks if the input is an empty string (evaluates to True if empty)
            raise Exception("You missed a price. Go back and input each price again.")
        elif not i.isnumeric():  # instead of `... == False`
            raise Exception("You missed a price. Go back and input each price again.")         
        
print(chocolatebill(CHOCOLATE))

A few points here:

• No input via the input method always results in an empty string (''), never in None
• Instead of returning stuff in the validation, raise an Exception. Ideally you even want dedicated exceptions, e.g. InvalidPriceError like

  class InvalidPriceError(Exception):
      pass
  
  raise InvalidPriceError("You missed a price. Go back and input each price again.")
  

  This makes your code much more expressive.
• sum(map(int, chocolates)) is valid for an arbitrary number of chocolate prices. Here sum returns the sum of elements in a a list-like element. map(int, chocolates) here maps the int method onto the chocolates list, i.e. trys to apply it to each element and returns a list of the result (i.e. a generator to be precise).
• I used an underscore before the _validate_input function because it is supposed to be a "private" method. I.e. it is supposed to be only used inside the scope of the chocolatebill function. This is a Python naming. convention.

There is even a lot more to mention here, but I don't want to stress you with too much information. I think this is already enough.