If you had a larger pipe leaving lets say your kitchen sink and it flows into a smaller pipe you risk plugs at the point where the pipe gets smaller. But going from smaller to larger is fine.

Now for proper sizing. You simply do not want to flow for any length of time out of a sink for instance on an over sized pipe. The volume of water that drains out of the sink will not be enough to carry any of the possible solids along with it, The result is bits of soil or in the case of kitchen sink bits of food will separate and begin to stick to the pipe. Over time the drain will become sluggish and being to plug up.

It sounds as though your doing this under the radar without permits. But someday the house will be looked at by a buyer and inspected. So I would suggest you consult with a professional plumber in your area and pay them a few dollars to lay out the pipe sizes for you and show you the proper types of fittings required for sewage systems.

You simply cannot put a Y connection in. It must be set at a special angle and connected correctly. Done wrong, you not only risk drain issues, but the inability to properly snake the pipe in the future if a clog does occur.

If you go to your local big box stores purchase a field guide for plumbing. It is called Code Check. This little booklet is not to expensive, but it will provide you with enough information to at least get an understanding on how to do this properly. http://www.codecheck.com/cc/index.html

if it isn't used very often.

Actually, the REAL story is . . .I don't use it all that much but what I do is

put my dishes in there to drain after hand washing so the majority of the water comes from the dishes dripping. However, I do run it through a rinse cycle every once in a while otherwise the standing water gets really icky (kind of "stagnant" like) but I still think way too much water is left in the bottom. I piggybacked this to Michelle's question and I KNOW I should have posted as a separate question.

I appreciate your input but I sort of suspect there may be something keeping it fromj draining as well as it should.

http://chemistry.about.com/od/toxicchemicals/a/Mixing-Bleach-And-Ammonia.htm

letting them dry between use is better but should still be avoided. only with thorough rinsing can the risk be reduced.