Mr Hutchison’s body was found at Port Edgar near South Queensferry at 8.30pm on Thursday, the day after he was last seen.
His family has spoken about his fight with depression and how he had helped others by speaking about his condition.
Frightened Rabbit tweeted on Monday for the first time since they paid tribute to the singer in a post on Friday.
They wrote: “Don’t ever think there isn’t someone out there who wants to listen to what you have to say. #MentalHealthAwarenessWeek G x”
The message has been liked more than 3000 times.
This year’s Mental Health Awareness Week, which runs from May 14-20, is focusing on the theme of stress.
Campaigners said research has shown that two-thirds of us experience a mental health problem in our lifetimes, with stress is a key factor.
A survey commissioned by the Mental Health Foundation found almost three-quarters (74 per cent ) of adults have in the last year been so stressed they felt overwhelmed or unable to cope.
The research also found more than a third of people (35 per cent ) had experienced suicidal thoughts or feelings because of stress.
On Friday evening, members of Frightened Rabbit visited the marina where Mr Hutchison’s was recovered and laid a floral tribute.
In a statement Scott’s brother Grant Hutchison, Billy Kennedy, Andy Monaghan and Simon Liddell said they felt “overwhelming sadness and pain” but the singer “leaves a legacy of hope, kindness and colour that will forever be remembered and shared”.
Mr Hutchison’s family said they are “utterly devastated” at his death and spoke of how he raised awareness about mental health issues.
They said: “Depression is a horrendous illness that does not give you any alert or indication as to when it will take hold of you.
“Scott battled bravely with his own issues for many years and we are immensely proud of him for being so open with his struggles.
“His willingness to discuss these matters in the public domain undoubtedly raised awareness of mental health issues and gave others confidence and belief to discuss their own issues.”
• If you are reading this article and are struggling and feeling that you have no one to talk to then please call Samaritans on 116 123