Resizing an EC2 instance requires stopping the instance, changing the instance size (more/less CPU/memory) and then start it again (steps here). For a single instance, this would cause a temporary outage of that instance.
To automate, AWS Systems Manager can run automations, including executing API calls. There's an automation document for resizing an instance you could leverage. In order for this to kick off in response to an event, you could create a CloudWatch to trigger SSM based on instance load (assuming you're logging the proper metrics to CloudWatch, by default CPU is tracked but not memory unless you enable it).
Instead of based on load, you could leverage CloudWatch to trigger events based on time, so if the backups occur on a set schedule, you could upsize beforehand and downsize after.
Regarding backing up, you could instead create and manage backups without causing any interruption by using AWS Backup to take snapshots of the instance's EBS volumes. Should you ever need the data back, you can create a volume from the snapshot to copy the data off or, if the whole instance needs to be reverted, replace the EBS volume from a prior snapshot.
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