Go for it. I've seen much younger folks than I who appear to be in good shape riding cross type bikes with enormous rear cogs and tiny chainrings. I don't know how much they use those gears but they're available.
Even though I'm fairly thin (5'11", 160 lbs, pretty close to my peak condition weight 40 years ago), I've never been a strong climber. No matter how much I work at it I'm solidly middle of the pack in climbing, and usually get dropped on hills by the local roadie B-group, even by folks who aren't much younger than I and some of whom are overweight.
So I swapped out my road bike's 42T small chainring for a 39. Helps a bit. I also got a 13-25 freewheel but the gear jumps were awkward so I swapped back to the original 13-24. I may try a 38T small chainring and a 13-28 freewheel. Won't make me faster on climbs, but I'll be less exhausted. In contrast my hybrid with 30/40/50 chainrings and 13-28 cassette climbs easily, even though the bike is heavier. So it's not just weight but having agreeable gearing.