Taking a bunch of hydrometer readings does expose your beer to a higher risk of infection, but if you have good sanitation practices it should not be a problem. But it does however waste a bunch of beer as good practice dictates the sample be thrown out and not returned to the vessel. If you have a refractometer you can reduce that wastage to a few drips each time, but don't forget it will not be accurate in fermenting wort and will need correction - there is a tool in Beersmith for that.
As for leaving it alone for 3 weeks to do it's thing - that is perfectly fine. That is pretty much what I do. I only take gravity readings when I think it is done or when I do a transfer to secondary. As long as the reading is what I expect I don't do any more. These days I only do a secondary if I am going to dry hop as I like to get the beer of the yeast before I add the dry hop.
Now having said that 3 weeks is not always going to be long enough depending on the beer you are brewing and the conditions you are brewing in, such as high gravity beers and the temperature the wort is fermenting at, yeast strain and health etc.
Also if something goes wrong it will take you 3 weeks to notice a stuck fermentation. But as long as you pitched a decent amount of healthy yeast into well oxygenated wort kept at the appropriate temperature you should not have this problem.