You can use the Set-AzureDeployment cmdlet to upgrade a webrole size, which you could then work into your existing PowerShell script. For instance, if you automatically deploy every customer web service/web role at a basic level/scale and then only upgraded them to larger capacity as needed, you could then use the following cmdlet as needed:
Set-AzureDeployment -Upgrade -ServiceName "MySvc1" -Mode Auto `
-Package "C:\Temp\MyApp.cspkg" -Configuration "C:\Temp\MyServiceConfig.Cloud.csfg"
I would envision you just adding a parameter to your current PowerShell script, and if specified, run the above cmdlet to Upgrade the Azure Web role.