ditching your weights is more applicable if you dive in colder waters and wear thicker wetsuits or drysuits and need a lot more weights.
yes, 1 or 2 weights doesn't sound like much now. But it would feel like 2 tons to you if you suffered a catastrophic failure and needed to do a CESA from 20m and your tank is dry.
yes by right you should have checked your equipment, by right you should be properly weighted, by right you should have more than enough air.
you did all of these, that's why you're able to do a second dive. but crap happens, that's why we have diving incidents.