I’m late to this thread, but I’ll add a few comments from a Brit. Firstly, yes, 63p is a ridiculously small amount for a note - but then 63p buys you a whole lot more in the US than it does back home, and I like that 
Second, how do all you Americans keep your dollar bills? I find that I quickly accumulate them, and end up with a wallet bulging with maybe 10 or 15 singles. That, combined with the fact that American bills all look so alike, makes it very hard for me to know how much money I’ve got on me - have I got a few twenties and tens in there or have I just got a bunch of $1 bills? Back home, it’s very rare that I’ll have more than 4 or 5 notes in my wallet, and if I do… well, I know I’m pretty flush and the next round is probably on me.
So, I have my wallet containing notes in my left pocket, and my coins in my right pocket. That way, if I’m making a small purchase (bus ticket, coffee, Tube ticket etc), I’ll reach for the coins, making it easy to get close to the right amount. This is easier now with the introduction of the two pound coin - it’s not unusual to have up to 10 pounds worth of change, and it’s really not that heavy.
However, I have noticed that the two pound coins are still relatively rare - I think a lot of people still “hoard” them, a situation that wasn’t helped when a rumour spread that those coins with a particular portrait of the queen were somehow more valuable. (They’re not.)
I guess as always it depends what you’re used to. My mindset is “notes = large amount of money”, so it seems strange to me getting a wad of low-denomination notes.
I must admit I’ve never seen a Sacagawea dollar. Are they really that heavy? Surely not heavier than four quarters? Since I’ve been in the US I seem to end up with loads of quarters, so surely swapping some of them for $1 coins would lighten the load?