According to www.b737.org.uk, the aspect ratio of the Boeing 737 increased from 8.83 for the -100 and -200 to 9.45 for the NG models (-600 to -900ER) while span increased from 28.35 m to 34.32 m. For the MAX, the wing span grew to 35.92 m and the aspect ratio to 10.16. The main reason is the higher price of fuel at the time of development of the more modern models which dictated a shift from a lighter wing to more efficient aerodynamics.
From this answer you will learn that aspect ratio is only the result of span and wing area, because those two parameters are the main drivers for induced drag rsp. fuel volume and are actively optimized to minimize overall cost. Today's very efficient engines allow to drive the optimum aspect ratio above 10 even for long-range airliners.
Early long range jets demanded high internal fuel volume, so their aspect ratio tends to bunch at the low end (7 for the B707-120 or the B747-100) while the 737, designed from the outset for short European and US continental routes, could afford a more slender wing. At the time of development of the original 737, jet fuel cost around 8 cents per Gallon. When compared to the peak in 2008, the nominal price has gone up by a factor of 50. While most fuel savings came from better engines, the higher aspect ratio of later 737 models contributed to keep them attractive for airlines (giving high rebates also helped).
To answer the question in your questions title, I plotted the aspect ratio (Y axis) over the different types (X axis) with data gleaned from Wikipedia. The higher values are for later types. With the exception of the 707, where the aspect ratio shrank from 7 for the -120 to 6.66 for the -320, the aspect ratio increased in all other cases for later variants:
Yes, the 737 started life with the largest aspect ratio of all Boeing airliners but the aspect ratio of the 777ER, the 787 and the 777X is higher than that of the B737 Next Generation (-600 to -900). However, the span increase of the B737 MAX let it take the crown back. The general wing shape, mass distribution or structure remain similar and have no consequence for the aspect ratio.