Is my anonymity at risk by not using HTTPS?
Yes; and any information you are sending should be considered compromised.
HTTPS (HTTP over TLS/SSL, or HTTP Secure) encrypts the data traveling between your computer and the webserver.
Even if you consider your communication being secure between your computer and the exit node, your data will be sent in the clear between the exit node and the webserver. Therefore, anyone monitoring the exit node you are using will see your data. If you want to know more about this, you can read Kim Zetter's article Rogue Nodes Turn Tor Anonymizer Into Eavesdropper's Paradise, 2007.
This does not directly break your anonymity; however, any information you are sending through HTTP might expose you. (Usernames, addresses, passwords, email addresses, etc.)
Indeed, Tor website mentions that you should use the HTTPS versions of websites:
d. Use HTTPS versions of websites
Tor will encrypt your traffic to and within the Tor network, but the
encryption of your traffic to the final destination website depends
upon on that website. To help ensure private encryption to websites,
the Tor Browser includes HTTPS Everywhere to force the use of HTTPS
encryption with major websites that support it. However, you should
still watch the browser URL bar to ensure that websites you provide
sensitive information to display a blue or green URL bar button,
include https:// in the URL, and display the proper expected name for
the website. Also see EFF's interactive page explaining how Tor and
HTTPS relate.
However, it clearly states at the beginning that Tor won't protect you between the exit node and the webserver:
the encryption of your traffic to the final destination website
depends upon on that website.
But, I am not sending any passwords or email addresses! I am not downloading/uploading anything! I am just looking at the content!
It doesn't matter.
First, I remind you that between the exit node and the webserver, the communication is not encrypted.
HTTPS uses Digital Certificate. This does not only provides encryption between you and the webserver; it also proves that the webserver has not been impersonated. You can see it as the ID you may have in your wallet: someone looking at it, then at you, should be able to confirm your identity. This is very important in terms of security. The messsage "This website does not supply identity information" means that the website did not provide any certificate. You have to trust that nothing wrong is happening.
It is not only about the data you send; it is also about the data you receive. Someone impersonating the webserver can show you anything he wants. He can put some malicious content inside the source code of the pages to reveal your identity. It has been done by the FBI when they seized Freedom Hosting. I admit that this example might not be the best one: Freedom Hosting was probably using HTTPS and not HTTP; but, as the FBI was able to seize the servers, they had total control over the data that were sent to the users. The point is: if you can control the data you send to the users, you can deanonymize them.
HTTPS makes it really hard.
EDIT: EFF.org has an interactive visualization of Tor and HTTPS.
