Your situation sounds exactly like mine, about 25 years ago. All the circumstances, including ASVAB and college experience are nearly identical. Your motivation (or lack of clear direction) is also familiar. The only things different is that you happen to be on the opposite end of the weight range and probably are not in danger of needing a height waiver.
I found the Navy to be exactly what I needed. In fact, I would have remained in the Navy, if I had not reached "high year tenure".
If your only concern about your recruiter is that he states your low GPA is not a problem, I don't think that is necessarily a cause for alarm. Some of the actual requirements have been posted in another thread (I can't remember which one), but as long as you have the proper high school classes, have not failed or repeated those classes, and have your high school diploma, then your recruiter may be correct in his assessment. You didn't mention if your 2.6+ GPA is from college or high school. If it is from college, I don't think that it is anything to worry about, unless it is a repeat of a high school subject that is required for the nuclear field that you have failed or repeated. If your recruiter tells you to omit some transcripts, it would be best to contact RCLCPO by personal message and obtain his assistance in finding another recruiter. But if your recruiter has not said anything like that and you have other concerns about things he has said, there are many ways to get an answer here.
Also, the particulars of your case (i.e., civil involvement, financial dealings, medical - including drug and alcohol involvement) are handled at the MEPS or District Office if waivers are required and your recruiter probably does not have a good idea if anything in your case (assuming he has told you to be 100% truthful) is absolutely disqualifying.
The Navy has many paths to help you fulfill your goals. Many times you just have to know what is available for you and you must ask for the opportunities. But at the same time, you must ensure that you keep your eligibility for the programs you are requesting and you need to work hard to give your superiors a reason for recommending you for any special program you are asking for.
So, it is a two way street. First you must define your goals and learn how the Navy can help you to achieve those goals. Then you must be successful in the way the Navy evaluates success and achievement. If you meet the requirements (whether they be physical requirements, test scores, a certain level of advancement through the ranks, etc), then there is a good chance that the Navy will allow you to achieve whatever goals you have set. (I say a "good chance" because, as with any other job, there are always those circumstances and coincidences that come up to impede some individuals from getting the most from their experience.)
I've probably been a bit long winded, but other than the similar circumstances, I haven't seen anything else specific that asked for a reply. You asked about current requirements, but first I'll say that not all conditions are disqualifying and if there is something that is not "perfect", your case will be considered on a case by case basis taking into account all the factors which might or might not make you a good candidate for the nuclear field. Requirements include possession of a high school diploma, high school algebra, not failed or repeated, no failed math classes, normal hearing, normal color perception, maximum 25 years old at time of enlistment, U.S. citizen, no civil involvement, no drug usage. Minor civil involvement or experimental drug usage are examples of conditions commonly considered for waiver.
There are many reasons to choose the nuclear field, but at this point, it's still best to add "if you qualify". I don't think the weight is that much of a concern. I don't know how physically active you are. If your're motivated enough, I'm sure you'll work on getting within standards. There are other requirements, such as color vision, that can affect you eligibility for programs, including the nuclear field. Some people don't know whether or not they meet all requirements until after they complete their physical examination and application screening at the MEPS.
Try the following thread for another discussion of nuclear field requirments:
http://www.nukeworker.com/forum/index.php/topic,3063.0.html