Small and lightweight are relative terms, especially when talking about six people living in the RV and traveling in the tow vehicle. Lightweight often implies trying to stay within the carrying and towing capacity of some van or SUV somebody has, but if you are willing to use a F-250 as a tow vehicle you have a wide range of travel trailers that could fit your need.
Six people in a F-250, four children and two adults, you can easily carry the tongue load of a 24-30 foot trailer of at least 6000 pounds, maybe as much as 8000 pounds with any F-250 offered in the past 15 years. Most configurations of the F-250 today will tow at least 12,000 pounds, some diesel models 14,000 pounds. For that many people, 24 foot is small, you will be converting sitting and dining spaces into sleeping spaces. Going on to 28-30 foot, there is either bigger living space or more permanent sleeping spaces.
There are hundreds of different travel trailer models in the 6000-8000 range, from almost all major manufacturers. For that weight range in sizes suited for a family, i.e. separate sleeping areas and maybe a bunk room, you will be looking at models built as lightweight rather than conventional, but that is most of what is on the market today. One manufacturer I know has tried to better accommodate families in smaller trailers is Keystone, particularly models in the Outback line that put a bed in a slideout room that come in over seating space for travel.
Whether or not a black water tank is too small depends on how you are using it and how often you dump it. Mine is just under 30 gallons, I need to dump every 3-4 days with two of us, every other day with daughter and two granddaughters along. But most of the time with family we are on the move each day and so can dump on the way in or on the way out of the campground each day. Most RV parks and many modern campgrounds have a place to dump at each campsite.
