I made union part hat that floats above the player's head, but it don't work, why?

So when I run this code, it works but, it makes the crown like 20 studs away from the player and is glitchy when the player moves.

local HatAttachment = script.Parent:FindFirstChild("HatAttachment")
local Handle = script.Parent
local Head = script.Parent.Parent.Parent:FindFirstChild("Head")
local Active = true

Handle.CFrame = Head.CFrame * CFrame.new(0, 0.5, 0)

while Active == true do
	
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.5, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.6, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.7, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.8, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.9, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 1, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.9, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.8, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.7, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.6, 0)
	wait(0.1)
	HatAttachment.CFrame = Head.CFrame * CFrame.new(0, 0.5, 0)
	wait(0.1)
end

Should I use a different way to set the crown position or a better way to animate it? Along with any reason why the crown gets set far away from the player?

Bare solution to the problem

You are multiplying CFrames, while you should only add an offset.

HatAttachment.CFrame = Head.CFrame + Vector3.new(0, 0.5, 0)

Better method.

Use an infinite tween. It is way more efficient, as tweens are handled internally in the engine. To make sure crown moves with player, use Motor6D and tween C0 property. Motor6D is how character's limbs are animated, without falling off.

You can safely remove hat attachment

--local HatAttachment = script.Parent:FindFirstChild("HatAttachment") -- you do not need that anymore
local Handle = script.Parent
local Head = script.Parent.Parent.Parent:FindFirstChild("Head")
local Active = true

Handle.CFrame = Head.CFrame * CFrame.new(0, 0.5, 0)

local weld = Instance.new("Motor6D") --this will be our new hat attachment
weld.Part0 = Handle
weld.Part1 = Head
weld.Parent = Handle

local TweenService = game:GetService("TweenService")
local style = TweenInfo.new(1,Enum.EasingStyle.Sine,Enum.EasingDirection.InOut,-1,true)
-- 1 second long tween
-- sine easing (like a pendulum)
-- direction in and out, so it eases at the beginning and end
-- -1 means infinite repeats
-- true means it will play in reverse once completed
local target = {C0 = CFrame.new(0,1,0)}

local tween = TweenService:Create(weld,style,target)
tween:Play()