Batteries will add weight, but you also get rid of diesel engines, traction generator/alternators, fuel tanks, etc which are all pretty heavy too.

On long routes the required size of the batteries might become prohibitive. But we’re talking about outer-suburban branch lines here which are usually pretty short, often only a few miles.

You don't have diesel engine and fuel tank on electric wired train ;) Also, looking at cars, batteries are much heavier than engines and fuel tanks giving same kilometrage. On top of that, fuel tank is heavy only in the beginning of the trip. You can fill up only as much as you need for the trip for better fuel economy. While batteries stay same weight for lifetime.

Batteries make sense for manoeuvre trains working ports, cargo train depots etc. Small batteries and recharge frequently.

> "You don't have diesel engine and fuel tank on electric wired train ;)"

In some cases you do because hybrid (bi-mode) trains exist too! [1] Although as another commenter points out, they are also working on tri-mode diesel/battery trains.

[1] https://en.wikipedia.org/wiki/British_Rail_Class_800

Batteries are still heavier than your typical commuter train diesel engine and tank. The diesel commuter trains are usually diesel hydraulic in Europe, so much less weight than you might expect, e.g. https://en.m.wikipedia.org/wiki/DBAG_Class_612

Batteries (or capacitors) would also allow the rheostatic braking to become regenerative and recharge them instead of just venting it as heat.

Of course, fully electric trains can just regenerate into the power lines.