Hey Yardenman!
So here is what I think is best to do in my experience at home and from what i've heard from other more experienced tomato gardeners. I don't think solarizing will actually solve your problem. In fact, I think it will do more harm to your soil than good because solarizing will inevitably kill all the microbes and organisms in your raised beds. Now while it may sound good, I have pretty bad news. For the most part, all of the most common types of problems that tomatoes get, including blight and wilt viruses and all those, are soil borne. The reason solarizing I don't think will help is because of the fact that they are pretty much anywhere and will make their way into your soil, my soil, and pretty much everyone's soils. I don't think trying to kill the first few inches of soil to kill weeds and harmful bacteria will actually do the job anyways as the bacteria will make their way up anyways.
Instead, I think there is a better and even beneficial way of fixing the problem. To avoid soil borne diseases and weeds, simply add a good organic mulch. It can be a good weed free straw, grass clippings from mowing a lawn, it can sifted or decaying wood chips, etc. Mulch is wonderful. It protects the soil from the sun, it holds moisture, it adds organic matter on top of the soil and adds fluffiness over time, provides a wonderful for bacteria and fungi, including the coveted mycrorhyzhaii fungi...im sure I spelled that wrong lol. And yes, it suppress most if not all weeds if you have enough of it. Plus, if you plant your tomato stems deep, this will allow more roots to grow into the organic matter too.
So i recommend a nice generous mulch a few inches thick. You can use compost, chicken manure, as well. Just cover the ground thick.
