The clover (assuming white clover) is spreading on its own because, most likely, the soil is low on nitrogen, which favors the clover instead of the grass. Clover can fix nitrogen from the air, so it thrives in the low-N soil where other things have a hard time competing with it.
According to this: Do legumes provide nitrogen to their companions? Clover will provide N to other plants (weeds) as it spreads, so you will probably never have a monostand of clover unless you kill everything and sow only clover. Also, the clover will never get tall enough to shade-out other established weeds. It competes by growing in places other plants won't. If other plants are absolutely thriving, its hard to see clover out-competing them.
Many weeds favor certain soil conditions. Like, for instance, yarrow will out-compete other plants in low potassium soils. What you have growing in your soil is what is favored to grow in your soil in its current condition. If you want to change the population of plants, change the composition of the soil to make it more favorable to one and less to the other.
If you want a stand of clover, mow low to keep the tall weeds in check. Clover thrives when mowed. Bag the clippings to keep the nitrogen low in the soil. Water deeply to wash away nitrogen. If you can, provide shade to shade-out other plants in favor of the clover, which likes shade (plant a tree to provide shade and use up N). All these things favor the clover and doesn't favor fast growing weeds (which need lots of N and light to grow fast).
There is nothing wrong with having a clover lawn. Some people prefer them (on the basis the clover adds nitrogen to the soil rather than removing it like grass would). Though, usually those interested in clover lawns are also interested in growing wild flowers and attracting a population of bees for their gardens. So, you have a fairly unique combination of requirements. I'm not sure how bees respond to clover flowers, but a lawn mower would chop the flowers off anyway.
Here is a site with more info on white clover: http://www.sare.org/Learning-Center/Books/Managing-Cover-Crops-Profitably-3rd-Edition/Text-Version/Legume-Cover-Crops/White-Clover
That site says "beneficial insect attraction", but I can't say to what degree from experience.