Two small napsacks and two (overhead-compartment-friendly) rolling bags. Would this be considered "bulky"?
There should be no problem storing that on a train where you have a reserved seat. (Since the trains with reserved seating generally have overhead storage and space behind the last row of seats).
You might feel awkward if you want to haul that cargo onto a commuter train during rush hour. (I occasionally see a person wheeling a large-size suitcase onto a sardine-tin train at 08.00am. People are polite about it - but you know they're frustrated). And if you're standing in a commuter train with a pack on your back, you can guarantee that someone is going to bulldoze into it with no regard to your comfort - they'll consider you very inconsiderate for not having removed it and placed it overhead.
You should also be aware that you may have to climb (and descend) flights of stairs in some stations. Lighter is better...