It depends what you want to achieve and what you mean by 'strength'. .
Heat treating can be used to increase the yield stress of a hardenable steel (to a greater or lesser extent depending on the alloy and process used). But what it won't do is to increase the stiffness of the part as hardening and tempering have no significant effect on the Young's Modulus of steel.
So heat treating will increase the stress at which a part will fail but it won't change how it deflects under load. In the case of a simple beam under bending load it will bend further before it fails but will still bend the same amount under the same load.
If you want to increase the stiffness and reduce weight you need to change the section for example a hollow tube will be much stiffer in bending than a solid one of the same mass per unit length and the same goes for 'I' sections. In other loading conditions webs, ribs and swages can be used to increase stiffness significantly.
In terms of material properties there is usually a trade-off between hardness and toughness (ie the ability to tolerate impact loading) and in some cases it is desirable to sacrifice a bit of hardness and ultimate tensile strength for the sake of ductility in order to prevent brittle failures which tend to be sudden and catastrophic.