First, what is a fossil? When an organism (living thing) such as a plant or animal dies, it lies on the ground. Over time it is buried in rock and it can be preserved and we call the rock remains a fossil. Let's talk about what factors DO affect fossilization.

1-- the type of organism. Hard things like bones and wood are easier to preserve than soft things, like skin or hair. That means that you're more likely to find the fossil of a snail than a slug.

2-- the type of rock it's in. Some types of rocks, like shales and mudstones, preserve fossils better than other rocks.

3-- how hot the rocks get.Sedimentary rocks are a great place to find fossils. But if a sedimentary rock is heated, and metamorphosed, the heat will usually destroy the fossils.

Now onto what DOES NOT affect a fossil. Things like the age of the organism, the organism's diet, style of movement (walking or swimming) do not affect how it fossilizes.

Fossilization happens when small chunks of rock (such as sand) enter the spaces in a body or plant that would have hosted resin, air, or soft tissue, preserving the body or plant. This is why a fossilized tree trunk looks like a statue of a tree trunk. For animals, bones decay much more slowly than tissue, so bones are better preserved as fossils. This is why fossils are typically dinosaur skeletons. Bones are also hollow, so sand can fill the interior of bones, making them last longer.

If a fossil is buried in the ground and protected from weather, it is not affected by weather.

There are too many factors that do not affect fossilization to list here. Factors that do affect fossilization include the presence or absence of hard parts, whether the environment is depositing sediment or eroding it, whether the chemistry of the environment is such that it would dissolve the materials being fossilized or not, the speed of burial, and many, many more.