One of the common problems when tarping utility trailers is that water can collect inside the tarp. If the top of your trailer is open, no amount of tightening will prevent this from happening. This won't necessarily damage the tarp but if the water sits there for a while it will start to get rancid and slimy. The weight of the water will also put stress on the grommets and trailer fasteners. If the water freezes, it could also expand and cause structural problems with the trailer or be too heavy to remove.
There are a couple of common strategies for preventing water from pooling.
If your trailer is open at one end, or if you can remove the tailgate to open up one side you could loosen the tarp at the open end in order to form a channel to allow rain water to run off. If you are planning to use this technique, make sure you order your tarp a little bit wider than you would otherwise so that there is enough extra material to make a proper channel.
Another option is to use boards (planks, plywood, etc.) to prevent the tarp from sagging into the trailer opening. In the example shown here, the back of the trailer is a little taller than the sides so we angle the last board so that it lines up with the back.
You could use one large piece of plywood on top but you might find that this is kind of heavy and awkward. It may be more convienient to use several smaller planks or even 1" x 6" planks instead.
Obviously these boards will need to be wider than the sides of the trailer so they don't fall in. Nevertheless, you don't want them to be too wide so you might consider adding angle brackets or some other form of clips on the edge of the boards to prevent them from falling into the trailer.
Once you have a solid surface on top of your trailer you can add your tarp and tie it down to prevent the wind from blowing it off. The rainwater should nicely flow off the sides.
Another potential solution is to arc the top of the trailer by adding bows so that rain water runs off to the sides. If you go with this option you will likely need to have a bow at least every two feet to prevent water from collecting between the bows. The bows shown in this photo are actually too far apart to be fully effective. Bows can be made of thin wood slats, copper piping or even PVC piping.