Yes it is possible to setup flat rate product shipping price based on product weight if you utilize shipping rules.
You can set product shipping to auto-calculated, than enter product weight.
When product shipping is set to auto-calculated, you can utilize shipping rules to setup shipping prices based on product weight in the cart.
For example you can have a shipping rule that reads:
Orders where total weight is greater than 2 charge $4.00 (followed by)
Orders where total weight is greater than 4 charge $8.00
This way orders of 3.99 pounds or less will have a charge of $4.00 and orders that weight 4 pounds or more will have a charge of $8.00
Steve - eez.io support