griz-up until right before this point, you are just making eye contact. When someone stares and you choose to stare back, now you are voluntarily entering into an inter-male aggression posturing ritual. Completely avoidable and needless.Some stare and I keep looking and my expression gets more serious. Some try to stare me down.
If you ignored their stare after the intitial eye contact and acted as if they didn't exist and weren't a threat, that would be the end of it (looking down like they intimidated you would be bad). Having stare-downs is why you've had those confrontations even at your big size. Your stare back challenged their ego, so they follow you and confront you, so you turn and confront them...so they; 1) insult, or 2) attack, or 3) leave. It's a process that can be broken at any time by either party when they don't wanna play macho anymore...until it goes beyond an alpha male ritual and someone decides to take it to the level of violence.
I'm only 5'10" and 185. I've never encountered a challenge like that. I've had people stare at me and insult me, but my response is to ignore them like an annoying dog. If they attack, I'll take them out...been trained to do it and training for it for quite some time now. Someday someone may follow and attack me anyway, but it won't be because I stared back and challenged their ego. When I ignore them they can save face by calling me names and thinking they're tough to my back. I don't act scared or tough...just indifferent. I'm aware of them and not concerned. JMO, if you make eye contact w/me I'll just nod back so it's no big deal...what ever works for ya.
Cool, related story that continues the "dog" theme; I met a guy with a huge, beautiful Akita up in Alaska. These are the dogs that were bred by Samurai to accompany them into battle. They are fearless and make great dogs to take while bear hunting. Anyway, the owner said a pitbull charged and attacked his Akita once. The Akita completely ignored the annoying little thing until it leaped. Akita latched onto it, snapped it's neck and continued on as if nothing had happened. Didn't stare it down, growl, bark or posture. Just took it out when it became a real threat and went about it's business (owner said he acted a little proud of himself ). The dog was very sweet, gentle and good with kids too.