[Duugu]

left button at frame background and draging = drag frame
left button at resize button and draging = resize frame
right button at resize button and draging = rescale frame

Rescaling is affected by horizontal mouse movement only. Someone has to implement the y axis.

It's not perfect but it's working.

Nevertheles I do agree with Vrul. Scaling a fame is never the best way to do anything size-related. In best case it just adds an extra level of complexity to your code. In worst case all your visible objects are a total mess.

[e] Didn't tested what would happen to child object of my test frame. And I'm seriously afraid of finding it out. ;D

tObj = CreateFrame("Frame", "testframe", UIParent)
    tObj:SetPoint("CENTER", UIParent, "CENTER")
    tObj:SetHeight(100)
    tObj:SetWidth(100)
    tObj:SetBackdrop({bgFile="Interface\\Tooltips\\UI-Tooltip-Background", edgeFile="Interface\\Tooltips\\UI-Tooltip-Border", tile = false, tileSize = 1, edgeSize = 10, insets = { left = 0, right = 0, top = 0, bottom = 0 }})
    tObj:SetBackdropColor(0, 0, 0, 0.75)
    tObj:EnableMouse(true)
    tObj:SetMovable(true)
    tObj:SetResizable(true)
    tObj:SetScript("OnDragStart", function(self) 
        self.isMoving = true
        self:StartMoving() 
    end)
    tObj:SetScript("OnDragStop", function(self) 
        self.isMoving = false
        self:StopMovingOrSizing() 
        self.x = self:GetLeft() 
        self.y = (self:GetTop() - self:GetHeight()) 
        self:ClearAllPoints()
        self:SetPoint("BOTTOMLEFT", UIParent, "BOTTOMLEFT", self.x, self.y)
    end)
    tObj:SetScript("OnUpdate", function(self) 
        if self.isMoving == true then
            self.x = self:GetLeft() 
            self.y = (self:GetTop() - self:GetHeight()) 
            self:ClearAllPoints()
            self:SetPoint("BOTTOMLEFT", UIParent, "BOTTOMLEFT", self.x, self.y)
        end
    end)
    tObj:SetClampedToScreen(true)
    tObj:RegisterForDrag("LeftButton")
    tObj:SetScale(1)
    tObj.x = tObj:GetLeft() 
    tObj.y = (tObj:GetTop() - tObj:GetHeight()) 
    tObj:Show()
 
    local resizeButton = CreateFrame("Button", "resButton", tObj)
    resizeButton:SetSize(16, 16)
    resizeButton:SetPoint("BOTTOMRIGHT")
    resizeButton:SetNormalTexture("Interface\\ChatFrame\\UI-ChatIM-SizeGrabber-Up")
    resizeButton:SetHighlightTexture("Interface\\ChatFrame\\UI-ChatIM-SizeGrabber-Highlight")
    resizeButton:SetPushedTexture("Interface\\ChatFrame\\UI-ChatIM-SizeGrabber-Down")
    resizeButton:SetScript("OnMouseDown", function(self, button)
        if button == "LeftButton" then
            self.isSizing = true
            self:GetParent():StartSizing("BOTTOMRIGHT")
            self:GetParent():SetUserPlaced(true)
        elseif button == "RightButton" then
            self.isScaling = true
        end
    end)
    resizeButton:SetScript("OnMouseUp", function(self, button)
        if button == "LeftButton" then
            self.isSizing = false
            self:GetParent():StopMovingOrSizing()
        elseif button == "RightButton" then
            self.isScaling = false
        end
    end)
    resizeButton:SetScript("OnUpdate", function(self, button)
        if self.isScaling == true then
            local cx, cy = GetCursorPosition()
            cx = cx / self:GetEffectiveScale() - self:GetParent():GetLeft() 
            cy = self:GetParent():GetHeight() - (cy / self:GetEffectiveScale() - self:GetParent():GetBottom() )
 
            local tNewScale = cx / self:GetParent():GetWidth()
            local tx, ty = self:GetParent().x / tNewScale, self:GetParent().y / tNewScale
            
            self:GetParent():ClearAllPoints()
            self:GetParent():SetScale(self:GetParent():GetScale() * tNewScale)
            self:GetParent():SetPoint("BOTTOMLEFT", UIParent, "BOTTOMLEFT", tx, ty)
            self:GetParent().x, self:GetParent().y = tx, ty
        end
    end)