There was a question on the community about bad Jira performance due to lot of attachments.
Well there are few things you can do.
- Symlink attachments directory to somewhere else like a dedicated file storage.
- Set a limit on the attachment size, I am sure you have it already, just review it.
- Do regular audit of your Jira instance to find out issues with big attachment sizes. I have seen instances where users have uploaded videos and big log files.
- Setup and archive strategy. Not sure if you are on DC already but move very old issues to another read only instance or may be delete them after storing backups.
There might be another issue causing memory or performance issues - like lot of configurations, too many custom fields and may scripts. Check this page for performance tuning.
To create symlinks follow this link from Atlassian.