I like @Caravanfan‘s answers. A sealed battery will remain the same. By charging it you just moved some electrons or ions from one side of the battery to the other.
You can also think of it like compressing a spring. The compressed spring has stored potential energy yet it weighs the same as a released spring.
For an unsealed lead acid battery, the answer is slightly different because of a “technicality”. A small amount of Hydrogen and oxygen gas is released when a lead acid battery is charging. You can see the bubbles on the plates if you take the caps off and look inside. Occasionally you hear about a battery exploding because someone had an open flame nearby and the Hydrogen ignited.
The acid water mix in the battery that has been broken down needs to be replaced occasionally to keep it at the proper level. That is why you need to check your car battery and fill it with distilled water.
How much hydrogen is released while charging and how much does it weigh? Think about how often you filled your car/motorcycle/tractor batteries – not very often but you do need to do it occasionally The typical lead acid battery will discharge 0.016 cubic feet per amp hour per cell. You can do the math if you want to take it further,
For factories that use battery operated forklifts the hydrogen released when charging can be a real safety problem .
Here is a Battery Hydrogen Concentration calculator supplied by Cisco, Inc that determines the hydrogen loss during charging and the concentration in the room.