Here's a picture of what weeping tiles do and stuff:
In the picture, it is raining.
The rain water percolates down into the ground. It would normally continue sinking into the ground until it hits the "water table" which can be anywhere from a few feet to a few dozen feet below the ground.
When the water table is high, then water will want to leak into any cracks in your basement foundation.
The weeping tiles allow an easier patch for the water to drain away. So, water in the water table above the weeping tiles drains into the weeping tiles, and there is no hydrostatic pressure forcing the water to flow into any cracks in your foundation.
(don't get me wrong. The ground around your foundaton will always be moist, but it will be the capillary pressure of the ground holding that moisture inside it. There won't be any excess water saturation above and beyond that which would create "free water", and create a hydrostatic pressure that would push water into your basement's foundation walls.)
Now, once water enters the weeping tiles, it will then flow to EITHER a catch basin (which is also called a "basement floor drain"), or it will flow to a sump pit. If you have a catch basin, that catch basin will have a p-trap at the bottom and that p-trap will connect to the main sewer drain pipe from your house (the one that goes to the city sewer pipe buried under the middle of the street your house is on). If you have a sump pit, then there will be a sump pump that pumps the water back outside, or into you're house's drain piping, depending on what your plumbing code required when your house was built.
If you have a duplex, then if there's no floor drain or sump pit in your half of the basement, it'll be in your neighbor's half of the basement.
Now, what happens if your weeping tiles get all clogged up with dirt? Well, then you have a situation where your weeping tiles can't do their job, and the result is that your house behaves just like there were no weeping tiles. In that case, excess water can build up in the ground around your house's foundation, and water will want to seep into your basement walls.
I'd phone around to some plumbers and see if there are any sewer inspection cameras that can be put into a floor drain or sump pit to check the condition of the weeping tiles.