I'd like to offer flat fee for orders between 0 and 5 lb.
 
I've tried to set this up in Custom Shipping with a new Shipping Type by specifying a minimum and maximum weight then entering a number in the Shipping Cost per order, but this calculates as a percentage of the selling price.
 
Any ideas?

I would have thought this would work providing you have no other shipping methods set up confusing the issue.
 
We do exactly the same only based on order value.
 
Have you tried adding a minimum and mximum goods cost also e.g
 
$0 to $100000
 
then the weight 0 to 5 lb.
 
then the charge e.g $10
 
then next
 
$0 to $100000
 
then the weight 5 lb to 10lb.
 
then the charge e.g $15
 
etc etc

There is also a setting for example above 5lb you can charge per lb
 
So up to 5lb $10
 
Between 5lb and 6lb you could set to $2 per lb e.g total = $12
 
etc etc

Thanks, freezer!
 
Well, THAT's interesting...
 
I set up the flat fee shipping in the "Custom Shipping" shipping module and have UPS active as well. Once I deactivated the UPS module, the custom shipping module worked fine.
 
I really need multiple shipping modules (like UPS and Custom Shipping) to be able to work together because I have an alternate way to ship that works by different rules (flat fee) and UPS (calculated fee) and want my customers to be able to choose between them. Also, I don't want to have products to be shipped by this alternative method to be mixed in (or submitted) to UPS.
 
The Custom Shipping method is set up with "Is External" unchecked and displays just fine (except for the price). It seems to be inheriting something from the UPS module (or something like that).
 
Any other thoughts?

Not sure to be honest it seems you probably have a more in depth system than we have. Maybe time to ask Viart perhaps.