What's actually happening
Low pressure at a tub faucet in an older home almost always traces to one of three things: corroded supply pipe, a scaled-up spout, or a tired valve.
The fastest way to narrow it down is to figure out whether the weakness is local to the tub or spread across the house.
Run the tub, then run a bathroom sink and the kitchen faucet. If they're all weak, the supply piping is the problem. If only the tub struggles, you're looking at the spout or valve.
Next, split hot from cold. Turn the tub to full hot, then full cold, and watch the flow. A one-sided drop usually means the valve or a specific branch, not the whole system.
Two minutes of testing here saves you from tearing into a wall you didn't need to touch.
The usual suspects, ranked
In a pre-1960 house, galvanized steel pipe leads the pack. The zinc coating wears off, the steel rusts from the inside, and scale builds until a 3/4-inch line flows like a 1/4-inch straw.
The tub is frequently the last stop on a branch line, so it starves before the sinks do. That's why folks notice the tub first.
Right behind pipe corrosion is the tub spout itself. Hard-water minerals cake up inside the spout and any diverter passages, and it happens gradually so you don't notice until the flow's obviously weak.
The mixing valve is third. Grit and scale collect in the cartridge or around the valve seat, and it usually shows up as one temperature side being weaker than the other.
Then you've got the boring but real culprits: a gate valve that isn't fully open, a corroded shutoff, or a failing pressure-reducing valve if your home has one.
Sediment kicked loose by recent plumbing or utility work rounds out the list. It's less common but easy to confirm because the timing lines up with the work.