To the Witness you are his/her "Bible Study...as in [My "Bible Study is progressing nicely"] Although they are likely very sincere and have pure motives, to the Witness, having you as a Bible study does give them a sense of accomplishment, not to mention some bragging rights in a way. Studying with you makes all the time they spent in the door to door activity worthwhile. It is also a means to count time without having to go from door to door work if they choose not to. Out of duty they are placed in the role of having to have all the answers to your questions. They are formally taught how to overcome your objections rather than understand why you might have them, see any validity in them or admit they may have them as well.
I'm curious if you have told them you visit this site. If you do tell them, they will likely say that visiting this site is at the root of your problems and that Satan is trying to blind your eyes or turn you away from God so that you will be destroyed along with his wicked system of things at Armegeddon.
I think asking them the hard hitting questions about Shunning and Blood Transfusions mentioned before, is important not because it will put them on the spot, but you really need to know the reality of their practices in these matters. Ask them if they think anyone who isn't one of JW's will survive Armegeddon. If they say yes....then ask why it's so important that you become one ? If they say no, ask them why at Armegeddon, a little child, who's parent isn't a Witness and an Axe Murderer, would both get the same punishment....death at the hands of a loving God.
If you are truly fed up with studying, the kind thing to do is to let them know so as not to waste their time. If you do decide to proceed, always have a plan B to fall back on. So many of us who were raised as Witnesses and leave have to start over from scratch.