I want a horse but I'm scared I'll be too heavy! help please?

I'm currently looking for a horse but I dono what would be ideal. I'm 1.62m high, so I'm shorter than average and I'm a little less than 80 kgs. So i'm chubby but not huge. i really want a horse but i'm terrified I hurt it. What would be an ideal horse for me? I'm not into hectic competing so I doubt i ever will. jus a casual hack and occasional jumping for pleasure.