I've never seen any evidence to back up the claim that smaller guys age poorly.
I'd easily change my opinion, if I see it.
Betts has some unique talents that I doubt anybody has ever studied- let alone how they do as they age.
I've heard Betts has amazing "twitch reflexes." How does that ability age? I sure as hell don't know.
First, what percentage of MLB players are categorized as "small" or "like Betts?" Then, is that percent about the same or worse among the best players beyond ages 32 or so?
This may not mean jack, but here are the top fWAR players from ages 32-36 since 1970:
41 Bonds
32 Schmidt
32 McGwire
29 E Martinez
29 Rose
29 Edmonds
27 O Smith
27 A Beltre
27 Kent
26 Suzuki & C Jones
24 Stargell, L Gonzalez & Larkin
23 Morgon, Bagwell, Palmeiro, Walker, Whitaker & T Phillips
22 Molitar, D Evans, G Brett, D Jeter
21 B Williams & J Cruz
20 ARod, Hendu, B Giles
Ages 37-41(which is actually beyond the years of the Betts contract)
39 Bonds
19 Aaron
15 Da. Evans
15 E Martinez
13 Papi & M Alou
12 W Mays, B Boone & J Morgan
11 C Fisk. Yaz & B Downing
10 O Smith, W Boggs
9 O Vizquel, S Finley, A Beltre, D Lopes, C Jones, P Rose
8 N Cruz, Hendu, J Kent
One could argue the second list blows your argument out of the water.