A "weak to strong" order is fine in general. But it always depends on group and encounter composition.
My expectation as a healer is, that the "most annoying" mobs are dealt first with. Like healers, guardians, stunnerm buffer, and mobs with large aoe's. Either use crowd control abilities on them (taunt, stun mezmerize), or kill them first.
In my opinion Kaon under Siege and Lost Island have several good examples why "weak to strong" isn't always the best idea.
Oh I'll agree on those, but in those cases you often need to explain about special NPC's beforehand, if they've never been there before. And if they have, then they got it, its fine.
What I'm more referring to is your standard, average trash pack in a flashpoint... 1 elite, 2 strongs and 4 normals/weaks. As a tank, I will usually lead with some aoe, tap everything once or twice, then hold the elite/strongs... but when the DPS tunnel vision the elite or strong, and let the weak stuff go for the healer, that's when everything becomes more work than it should be. Now I have to burn taunts, or the healer has to heal more than they should be healing, all because DPS doesn't have common sense.