Some caveats to the advice above.
Yes, BA does search for passengers who end itineraries early. What it does about it is likely vastly different to what happens with, say, AA.
AA is reasonably well-known for identifying persistent offenders and even accompanying them to the gate for their next flight to make sure they don't get lost. BA won't ever do that, but it does have certain options available to it.
If you book direct with BA, and don't make a habit of doing this, then it's almost certain nothing will happen.
If you book with a Travel Agent, BA has the option of charging that TA the difference in price. It has history of doing this - see
Our EX-EU Horror story. The agent may, under their terms, have the option of charging that back to you - so the risk is much, much higher of being dinged. Even if you don't personally get charged, you may consider you have a certain duty to that TA to take the last flight, particularly if you want to use them again!