Can anyone cite the detail in the regs regarding awarding a second marksmanship badge if a Soldier only is assigned one weapon system?

Interesting question. But I recall wearing the Expert Badge in Grenade and Sharpshooter in Rifle during my Class A inspection during Basic Training. The Rifle was my assigned weapon system, yet I am fairly sure that the Grenade was not an "Assigned" weapon. Taking that logic, I would make the case for having two different qualification level badges for two weapons, even if only assigned one.

USMC is pretty straightforward. One badge for rifle, one for pistol. The classifications from best to worst are Expert (crossed rifles), Sharpshooter (iron cross), Marksman (pizza box). The only one eligible for any bar below is Expert. It designates how many times you have fired Expert, such as 5th award rifle, 3rd award pistol, and they wear the bar below the respective badge. After that, shooters that have earned awards from competition matches can wear them in place of or along with the others and there are too many possibilities to explain in detail. They can be from placing in Division Matches, Inter-Service, Camp Perry Nationals, or International. Once a competition shooter earns enough points they are classified as Distinguished and wear a Distinguished Badge. A competitive shooter may be Double Distinguished when they reach the mark for both rifle and pistol, and they wear one for each. There are also badges for various accomplishments in marksmanship as shown on the page linked to. No badge for grenade but if someone goes UNQ (unqualified) with grenade their survivors get the SGLI...okay j/k but you get the idea hopefully.

https://en.wikipedia.org/wiki/Badges_of_the_United_States_Marine_Corps

Found it! If anyone care to know I have it below. Now just to see if the BN or BDE have a policy of not awarding the second badge/bar.
AR 600-8-22
Section IV
Marksmanship Badges and Tabs
8–47. U.S. Army Basic Marksmanship Qualification Badges
a. A basic Marksmanship Qualification Badge is awarded to indicate the degree in which an individual, military, or civilian has qualified in a prescribed record course and an appropriate bar is furnished to denote each weapon with which he or she qualified. Each bar will be attached to the basic badge that indicates the qualification last attained with the respective weapon. Basic qualification badges are of three classes: Expert, Sharpshooter, and Marksman. The only weapons for which component bars are authorized are in table 8–2. Basic Marksmanship Qualification Badges are awarded to U.S. military and civilian personnel, and to foreign military personnel who qualify as prescribed.
b. See AR 670–1 for instructions concerning the wear of basic Marksmanship Qualification Badges and component bar tabs.
c. Approval authority is as follows:
(1) Any commander in the rank or position of LTC/O–5 or above may award to Servicemembers of the Armed Forces of the United States; camp and/or post commanders, Professors of Military Science, and Directors of Army Instruction and/or Senior Army Instructors.
(2) Except for uniformed civilian guards (AR 670–10), awards to civilians will be made by the CMP. The CMP is administered by the Corporation for the Promotion of Rifle Practice and Firearms Safety, Inc., Post Office Box 576, Port Clinton, Ohio 43452–0576. The authorization for civilian guards to wear basic Marksmanship Qualification Badges may be made by installation commanders. Civilian guards will procure badges at their own expense.