Old stuff on twitter is weird. Tweets seem to eventually forget that You specifically liked a tweet, and will allow you to like a tweet again, and the like count will reflect you liking it twice.
Like count is almost surely just a locally incremented number, your like request will eventually get processed and will be dropped if it was already liked. It only has to be an eventually consistent value.
This is beyond optimistic updates (which twitter also has plenty of issues with - you'll reply to your tweet and it'll jump immediately to two replies, but on refresh just show your one).
