Trainer told me i shouldn't heavy lift because my back is too flexible(gymnast grade)& it may be why i have back pain(weak core). how to decrease flex?

Strengthen core: You don't have to lift heavy to strengthen your core (and all of your muscles). You can gradually increase weight as you get stronger. Have you seen those flexible gymnast's muscles? So, your flexibility being what it is (and not necessarily bad), have you discussed your back pain with your physician? Might be a good idea to get medical input and exam in addition to your trainer...