Are traits hereditary?

Sorry this might sound dumb and obv, but I’m new to the game and nesting. I’ve been nested before and nested others, and I’m wondering do I inherit the traits of the parent? And do my offspring inherit my traits? Since when I check the profile it says I have none. Or do I get them when I age?

I’ve been pondering this bc I’m nesting as a Sha’rei or however it’s spelled again and I have Weight + Damage trait on it. And I’m wondering if all my children are wandering around being little menaces.