Make great/much play of something
Definition 1 of 2
Pro Tip 1/3Subtly Criticizing
Can imply disapproval by suggesting someone is overemphasizing something trivial. 
She made much play of her minor role in the project, which irked her teammates.
Pro Tip 2/3Conversation Focus
Used to steer a conversation toward a particular subject the speaker wants to highlight. 
During the meeting, he made great play of his department's success to impress the investors.
Pro Tip 3/3Emotional Impact
May emotionally charge the conversation, for positive or negative effect. 
She made great play of her hardships, eliciting sympathy from the audience.