(FilteringEnabled) How to make this Touched script add a higher value to a player's stats?

The problem might be that the berry is touching something other than a player's character (such as the ground), which causes the script to execute HitAlready = true, even though this should not happen. To fix this you could change your code to

--ServerScript
local HitAlready = false
script.Parent.Touched:connect(function(hit)
    local Player=game.Players:GetPlayerFromCharacter(hit.Parent)
    if Player==nil then
        return
    end
    if not HitAlready then
        HitAlready = true
        Player.Stats.Fullness.Value = Player.Stats.Fullness.Value + script.Parent.Hunger.Value 
        Player.Stats.XP.Value = Player.Stats.XP.Value + script.Parent.XP.Value
        Player.Stats.Health.Value = Player.Stats.Health.Value + script.Parent.Health.Value 
        script.Parent:Destroy()
    else
        print("Berry already touched")
    end
end)

Since you are making the call script.Parent:Destroy(), you don't even need HitAlready; the touch connection will automatically disconnect after the berry is destroyed, so players can't hit it again. Hence, your code can be simplified to

--ServerScript
script.Parent.Touched:connect(function(hit)
    local Player=game.Players:GetPlayerFromCharacter(hit.Parent)
    if Player==nil then
        return
    end
    Player.Stats.Fullness.Value = Player.Stats.Fullness.Value + script.Parent.Hunger.Value 
    Player.Stats.XP.Value = Player.Stats.XP.Value + script.Parent.XP.Value
    Player.Stats.Health.Value = Player.Stats.Health.Value + script.Parent.Health.Value 
    script.Parent:Destroy()
end)