All In One WP Security no database backup possible

Hi,

First very important: my understanding of WordPress is very limited. I can’t code and have not a lot of knowledge about how all this works. Please be specific where and how I can solve the problem, so I don’t have to re-ask again. ??

I do have All in One WP Security Plugin running. The last database backup the plugin made was at 24.12.15. Since then no backup was made. I tried to do a manual backup but get the following message:

Fatal error: Allowed memory size of 268435456 bytes exhausted (tried to allocate 72 bytes) in /home/SERVER NAME/www/artcascadea.ch/wp-includes/wp-db.php on line 2347

I looked up on my server and this is what the mentioned line 2347 says:
$new_array[] = array_values( get_object_vars( $row ) );

I do have also installed the WP-Optimize plugin. After clean up it shows me: Current database size : 27.1 MB

Why is my database size so big?
Is there a way to reduce the size?
How can I increase the allowed memory size and how high should I set it?

Here is the link to my site: artcascdea.ch

Thank you very much in advance for any help!