Hi there,
thats perfectly normal – aside of the wayback site using a rendering engine which may not generate the exact same results as your modern browsers.
But the main reason; wayback takes a snapshot of the site at the given time, this snapshot includes any links to your sites style sheets etc. If those links no longer exist, for example they were combined in a cached file, then it will fail to load the styles.
If you inspect the Wayback site with the developer tools you will see some Console errors, one of which is a 404 status to the original sites cached CSS file.