If you can press in the bottom of the sole with your thumb, the soles are probably too soft to give your foot proper protection. Trails are not like the pavement in front of your home. Trails are rocky, and you need good protection to avoid bruising the bottom of you feet. Good boots provide good protection on the sides. They are heavy because they either have extra padding to protect your foot from stones, rocks, and branches you may step on which could gouge into the side of the boot.
Good boots provide good ankle support.
Grab the top of the boot and try to bend it over side-ways. If it bends easily, it's probably not going to provide the level of protection needed on the trail. The top of the boot should be stiff to hold the ankle in place and provide it with good support. Good boots are either waterproof, or are capable of being waterproofed with special waterproofing solutions. I would avoid fabric boots that are not waterproof.