Economics drove the values on the Tweed. Electrolytic caps were expensive early on. Smaller valued caps were cheaper and plentiful. As they went down in price, amp manufacturers started using larger sizes, usually capping at 40uF so as to not stress tube rectifiers.
What difference does the larger values make, lower hum, "tighter" bass, less sag?
All those things. Some designs sound more sterile with larger caps. I built a 5F1 Champ out of salvaged radio parts and used the caps that I normally stock for Blackface/Silverface designs. The filter cap that decouples the preamp ended up being a 22uF, and the amp just didn't sound right so I replaced it with an 8uF while leaving the rest of the caps at 22uF and the amp sounds great!.
More to the point if an amp design has 40uF caps, what would the effect of putting 10 uF's or 16 uF's be.
More power supply noise for sure, however the amp should be a little more "loose in the low frequency" and Saggy. My personal preference is to use the higher (black and silverface) values in the power section and use the smaller (tweed) values as filters for the preamp. I think it gives the best of both worlds.
I have built a few amps with too little filtering in the power section (2x 22uF in Series for 11uF) and I never liked the result. There was too much power supply noise. Bolstering that up to 40uF while using ~10uF in the preamps always sounds great to me in Fender-style amps.
j.