Franklin's aphorisms were typically practical wisdom which the reader could apply to his own life based on his own experience and common sense. A "leak" in a person's own life might be interpreted as a small recurring expense that can add up to many hundreds or thousands of dollars over the years. An excellent example is cigarette smoking. Cigarettes are now selling for what seems to older people like myself the astronomical price of around five dollars a pack. Not a carton, but a pack! If a man started smoking only one pack a day at the age of twenty, he would be leaking $1825 a year out of his pocket, and if he continued smoking at the same rate for fifty years, assuming he managed to live that long, he would have leaked $91,250. But that would only be in capital. He would also have lost all the interest and compound interest he might have accumulated in that time. Furthermore, the price of cigarettes would probably continue to rise, and he would almost certainly increase his craving for nicotine over the years, so that he would be smoking two packs a day and maybe even three. In his lifetime this one "leak" could cost him as much as half a million dollars.
Most of us have "leaks" in our personal economies. As we get older and earn more money, we tend to develop more and bigger leaks. It makes good sense to look at our own lives, rather than worrying about Great Britain's or China's "leaks," and see what we could do to stop any small leak that is obvious. Americans are probably the most wasteful people in the world, so it should be easy for most of us to spot leaks. Examples that come to mind are unnecessary auto trips to the supermarket, leaving lights on in an unoccupied room, leaving the television set playing when nobody is watching it, putting too many postage stamps on a letter, using too much laundry detergent, wasting food, making unnecessary long-distance phone calls. In one of his essays (from which Franklin no doubt borrowed more than once) Sir Francis Bacon says to be especially cautious about incurring regular small expenses rather than worrying about big one-time expenditures. A one-time expenditure is not a leak, but a recurring small expenditure can definitely be described as a leak if it can be stopped.
To add to the comment written above, notice that proverbs or common sayings using different metaphors often have a common message.
In this case the point of vulnerability is a leak in a ship. We can express the same thing by talking about the weakest link in a chain, for example. ("A chain is no stronger than its weakest link.") Another similar one is "For want of a nail a country was lost." (There is a whole poem to this effect!)
The lesson of fixing problems before they get even more complicated also could be highlighted. In this case "A stitch in time saves nine" comes to mind, or "An ounce of prevention weighs more than a pound of cure," or even "Nip it in the bud."
Sometimes proverbs even contradict each other! Consider, for example, "look before you leap" compared to "opportunity only strikes but once." The first commends foresight and prudence; the second, courage and expediency!
The moral that is being taught is that a very slight moral infraction can cause the downfall of a very strong person. As an example, there is a very wealthy and intelligent man who seems to be very successful on the outside. His wife loves him; his children love him. The people at his company love him. He is well known in the community and everyone respects him. But he has a little problem....(I won't say what it is because it could be anything.) This "little" problem affects every aspect of his life. He won't admit it to himself or others. He won't work to try and overcome his one little character flaw. However, in the end it causes him to loose everything.
This aphorism is a great writing prompt because you could write a tragic story built on this basic premise.
The above answers are excellent. I have one additional point to make, and that has to do with time. A small leak in a great ocean liner can go unnoticed for weeks. Unattended to, however, the ocean liner will fill with ocean water, begin to list and eventually sink.
Once, over five million years ago, in what is now Arizona, there was a lit trickle of water that became a stream, and that stream became a river. The river cut a shallow path into the red-brown crust of the earth. Over ages and ages, the river washed away more and more earth and cut into the rocks. Slowly, incessantly. The Grand Canyon is a monument to the power of water and time.