You would need to contact your host.
Based on what you tell me, your host is using up as much physical memory as the size of your site's files. However, Akeeba Backup runs in small and discrete steps, each one backing up a few files. The way our algorithm works, its maximum physical memory use is under 32MB (typically well under 20MB).
I do know why your host may end up using up all of its physical memory. It is probably using CloudLinux which has a major bug that's confirmed since at least 7 years ago and marked as something which won't be fixed. A normal server makes use of the free memory (memory that applications don't use) for disk caching. When applications need memory and there's no more free memory the Operating System will take memory from the disk cache and assign it to the application. There's no latency between memory pressure and taking away memory from the disk cache.
CloudLinux has a bug which prevents it from doing that. Once the memory is used for disk caching it will take a long time, in the order of several minutes, before it decides it should deallocate memory from the disk cache. When you are running a backup – even when simply using tar from the command line – this bug will cause physical memory exhaustion.
There is no solution to this problem. It's a problem inherent to the design of CloudLinux.
A workaround is to exclude the big images folders from your main backup profile. Then create 2-3 backup profiles with their types set to Files Only, each one backing up a portion of the images. Automating these backups would require scheduling them so there's an at least 30' gap between one backup finishing and another starting up.
Again, this is a problem with the design of CloudLinux, nothing we can do about it. Because it's a problem at the OS level you won't be able to use any other backup solution either, be it a plugin or even command line tools.
If you're wondering, yes, it took me several days of head scratching to understand this problem when I first encountered it circa 2014. It is a very rare problem but it can and does happen with larger sites. IMHO a site as big as yours shouldn't be on a shared host. If you are NOT on a shared host then your hosting company shouldn't be using CloudLinux for a managed server.