Backup Error Due to PHP Memory

Hi, I keep receiving this error message when attempting to complete a backup via the plugin BackWPup.

PHP Fatal error: Allowed memory size of 268435456 bytes exhausted (tried to allocate 239861761 bytes).

I recently made the switch from WordPress.com to WordPress.org, so am self-hosting for the first time. My site has not been backed up since the switch due to this error, aside from exporting my files until I resolve this.

To fix – should I be concerned with reducing my PHP memory, increasing my PHP memory or finding a new backup plugin so I don’t need to touch the PHP memory on my site at all?

I want to be able to provide more information about my current PHP memory, but I’m not sure where to find that. To try and get a sense, I installed the plugin P3 – Plugin Performance Profiler, which ran a scan. If it’s helpful at all, results show: Number of PHP ticks:12,548 calls avg. RAM Memory Usage: 39.49 MB avg.

Thank you!