The objective lens is the most important aspect of your rifles cope and serves to transmit light back to the ocular lens located in the eye piece.
The larger the objective lens (ie. 50mm -75mm), the more light it allows in which allows the user to shoot in low light conditions but also the more weight it adds and the more cumbersome they become.
That being said, you probably won't notice the difference in weight between a 32mm and a 40mm.
The choice of the size of the objective lens is probably not as important as asking yourself what the price range is for your rifle scope.
If you are looking for rifle scope under $100, you probably don't have a whole lot of choice of the specific objective lens size. Once you get up to under $500, it opens the range of objective lens sizes up.
Overview - Objective Lenses
For a medium power rifles cope, 30mm – 42mm is pretty standard and will perform well in a variety of conditions.
I would suggest this is the most popular range and very good for most hunters and target shooters.
It will allow enough light in to provide clarity throughout the magnification range, but it won’t be mean that the scope becomes cumbersome and overbearing.
Remember, the scope will add weight to your setup and you don’t want to be packing around extra weight or have the rifle not feel comfortable when firing.
If you are using the firearm at the range only and have a bipod or some other gun rest, then weight may not be your primary concern.
Budget - Objective Lenses
Not always the case, but with higher powered and more expensive rifle scopes, you may be more suited to a 50mm + objective lens.
For instance, the Millet LRS is a tactical long range scope that is very capable of shooting at 1000 yards, comes with a 56mm lens.
It is designed for higher calibre firearms (ex. 50 BMG) and will provide shooters with a crisp and bright field of view at high magnifications.
For additional information and help choosing the right scope, see A Complete Guide to Choosing the Best Rifle Scope (including Top Riflescope Reviews).
Stay safe, and happy shooting!