Tyvek is the name for a variety of sheet products besides House Wrap. Regular House Wrap weighs about 2 oz per square yard. There is a product called Kite Tyvek that weighs about 1.3 oz per square yard and has about the same water resistance as does the House Wrap type. At this site http://www.intothewind.com/shop/Fabric_for_kitemaking_or_kite_repair/Tyvek
you can buy it in quantities as small as one running yard; you have to pay for shipping though. I find that the kite Tyvek is more like cloth than is the House Wrap and a lot less noisy when you lie on it. All Tyvek, however, is subject to "static cling" which means that a lot of organic particles from the soil surface will cling to it. A good shake will get rid of most of it though.