First thing first, 503 “Service Unavailable” is a page not found response code. Much more like, 404 page.
According 10 Status Code Definitions,said that:
10.5.4 503 Service Unavailable
The server is currently unable to handle the request due to a temporary overloading or maintenance of the server. The implication is that this is a temporary condition which will be alleviated after some delay. If known, the length of the delay MAY be indicated in a Retry-After header. If no Retry-After is given, the client SHOULD handle the response as it would for a 500 response.
Note: The existence of the 503 status code does not imply that a
server must use it when becoming overloaded. Some servers may wish
to simply refuse the connection.
Do you should worried about this problem? Well, it's up to you. Better thing to do is try to summarize your post and only display most relevant post on your homepage, choose light weight template and images, last but not least run speed test of your blog.
That is all I can review about 503 “Service Unavailable”.