Enneagram 6 Health Levels

Under Stress (Six Goes to Average Three) Sixes are often visibly nervous, reacting with self-doubt to situations and getting caught in over-thinking a problem. When stress escalates beyond the normal level, however, they jump into action—and stay in action, trying to deal with their anxieties by working harder. If, for example, they feel pressured at work, Sixes may spend their weekend frantically doing yard chores or obsessively reorganizing the closets as a way of discharging or avoiding feelings of inadequacy. They also fear letting others know how overwhelmed they are, so they may take on a false persona of competency and efficiency, like average Threes. ("Don't worry about anything. I've got this handled.") They focus increasingly on tasks and on being efficient while cutting off from their feelings so that they can stay functional, but this can lead to major emotional problems for them and for their relationships. 

Security (Six Goes to Average Nine) In situations where Sixes feel secure, they begin to deal with stress by simply shutting down and becoming indifferent to their surroundings, like average Nines. They do not want to be disturbed or bothered by loved ones—they feel that they have been working hard and they experience virtually any kind of interaction as another source of pressure. They will be pleasant one moment, but can suddenly become stubbornly resistant and shut down in the next if they feel that others are demanding something of them. At such times, Sixes become unavailable and passive-aggressive, not wanting to respond to others or to move out of comforting but numbing routines. 

Integration (Six Goes to Healthy Nine) As Sixes learn to trust themselves more, they also become more open to life and to other people. They gradually learn to relax their hypervigilance and simply be with themselves or with whatever life is presenting in the moment. They gain a deeper acceptance of life's ups and downs such that they are not riddled with dread and anxiety. They are inclusive and supportive of others—and much more at peace. Integrating Sixes are able to let their minds rest in their natural, pristine state of clarity and inner quiet. They are able to stop second-guessing everything and let their own inner wisdom arise. The result is that they are more serene, grounded, and joyous—light and stable.

I'm a 6w7 tritype 649
and apparently, I read this somewhere sketchy and very unreliable but I agree nonetheless, that 6w7's have a stronger link to e3 when moving towards integration. They move out of passivity, procrastination, and enjoyable distracting activities (?) and do what really needs to be done.
It could also be that when moving towards healthy levels, enneagram 6 has elements of both 3 and 9.