Please define "catch weight", is this fishing or sports related?
Shopify does not have weight based selling features
The exception to the below is if you can simply invoice or use draft orders in which case you can just enter a custom price per order.
If your primary business products are fixed product titles and sold by weight via an online store and you have not began with shopify I'd recommend finding a different platform, shopify simply isn't built for that mode of sale , or other dimensional modes, and you will have constant headaches reconciling everything.
Notice if you can just make a custom product per customer or per order this is not an issue, it's mainly a problem when you want to have the product data entered for customer to self-checkout through the online storefront.
If you do mean simply selling a product by weight and must use shopify you will basically need an app and/or advanced theme customizations to do so with shopify currently. Apps would either be custom apps or some automation app to coordinate inventory.
Alternatively you need to structure the product so the quantity IS the sell weight and do heavy theme customization including notifications, and if on shopify Plus change the checkout experience.
Example - Product Quantity Method
If a merchants sell by the pound they would need each "quantity" to represent 1 ounce and you add 16 ounce "quantities" to the customers cart then of course may need backend automation apps to coordinate inventory, further info found by researching the forums or through consulting.
POS ONLY
If this is for Retail and you must sell by weight Derrick of filljoy has made an app for POS only
https://apps.shopify.com/sell-products-by-weight
Card holds
Make test orders to see the overall process depending on payment gateways.
Using shopify-payments the max capture period is 7 days.
You will need any products to be the maximum price possible , otherwise initially with a low price that you then need to raise customers will have to go back through checkout when the order total increases.
Alternatively if you have the payment information on file then when using Draft orders you can finish payment in the admin that way, incurring processing fees for manual processing.
https://help.shopify.com/en/manual/orders/create-orders#accept-payment
Goodluck!
