Additional to the above, the 737-300 wing was designed decades before the 777 wing and the efficiency advantages of the newer creation are significant - Winglets, vortex generators, etc, are not as necessary these days due to modern wing technology improvements.
Span restrictions due to
airport infrastructure are few and far between given most airports/aerobridges/tarmac areas easily cater for 707s, A320s, etc, etc also. I think that's what you meant??
Adding a winglet to an old design is a relatively cheap measure to lengthen the relevance of an old design, just like hush-kitting or re-engining. Also helps puts off the possibility of the operator (customer) buying a new machine from a competitor.
Whether the aerodynamic advantage greatly outweighs the physical
weight penalty of the winglet, itself, on short-haul ops is for the bean-counters to wet themselves over, I sure wouldn't know.
As for looks, personally I believe having winglets of any shape or size, particularly the Airbus style, "spoils the look of the thing", as 'Moggy' Cattermaul once said.
Raked tips are definitely shnazzier.
While I'm at it, jet engines should always be at the back...
