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Gutter overflowing in the middle

We've got a ~8 year old house with on one side a ~20 meter gutter with two down pipes at either end. During heavy rain, the gutter overflows in the middle. It never seemed a big deal, but during a recent storm we noticed it had leaked to the inside as well. Also, this gutter always has a lot of dirt built up, and plants start growing in it quickly, which may indicate a problem with the angle. I've installed water tanks at both ends which catch the rain. However, the adapter decreases the down pipe size about 50%, so this may contribute as well. Perhaps a second pipe would help. So, there are two issues, that it overflows, and that it happens in the middle (and not at either end).