Not being a gardener myself, I'm going mainly by what I've heard others say. I think they say something about the competition for water, nutrients, and sunlight. I think it has something to do with allowing the plant to produce its fruit.
The visual effects are obvious to even me. I've seen gardens that were so over run with weeds, it made me wonder at the lack of care. The beauty of the flower or the tasty fruit seem of little value to the caretaker. It is not a garden at all, but an unsitely, unorganized mess. Have you noticed that weedy gardens look worse than almost anything growing naturally?
Jesus said something about the affect of weeds. First, as a part of the parable of the sower of seeds...
"...and some fell among thorns, and the thorns sprang up with it and choked it." (Luke 8:7)
Then He explains...
"Now the ones that fell among thorns are those who, when they have heard, go out and are choked with cares, riches, and pleasures of life, and bring no fruit to maturity." (Luke 8:14)
What do people see in me? An ugly, weedy, unfruitful mess? Do they see wasted talents and resources? Unfullfilled potential? Someone who is distracted and tangled-up by the weeds of this world?
It is time to do some weeding. I'd rather display the beauty of Godly character and bear the fruit of righteousness. A productive garden takes diligent work. It requires discipline and focus. These things are so easily neglected when we let our eyes wander and our minds stray for even a moment.
Maybe that is why Jesus answered the question about which is the great commandment like He did.
"You shall love the LORD your God with all your heart, with all your soul, and with all your mind. This is the first and great commandment." (Matt. 22:37-38)
Work. Discipline. Focus.