Family dynamics are often more powerful than we realize: it can be very hard to change patterns that are decades old. I suspect that passive communication with your brother will
not work. If you step back to give your brother a chance to do more, he might not notice, even though to you the shift is dramatic. It's likely to be much more effective if you speak to him directly and try to negotiate a new understanding regarding your mother's needs.
Before you speak to your brother, develop clear goals for what you hope to accomplish. Is the burden of caring for your mother too much for you, or is it primarily an issue of fairness between you and your brother? Is the amount of time you spend with your mother creating problems in your marriage? Are there specific tasks that you'd like your brother to take over, or is there a way you can alternate responsibilities? If you come to the discussion with clear ideas about what isn't working and how the situation could be improved, you're more likely to get results.
Approach your brother in a non-accusatory way, if you can. Focus on the fact that you need help and stay away from issues of right and wrong, and good guys and bad guys. If your characterization of your brother is accurate, that is, that he tends to let others do most of the work, than you probably shouldn't expect a significant change in his behavior. Still, if you’re specific about how he can share your mother's care, he'll be more likely to rise to the occasion. If he can't spend more time with your mother, would he be willing to pay a housekeeper, for example, so you don't have to spend your weekends cleaning your mother's house? Try to play to his strengths. Is he good with finances, for example? If so, ask him to take over your mother's taxes. If it would help you (and your marriage) to have regular weekends free, propose a schedule for alternating visits.
You may be surprised by what comes out in the discussion with your brother. He may believe that you're both doing an equal share of the caregiving tasks, for example. Or it may turn out that he believes your mother always favored you, and he doesn't believe she wants his help. You may find it helpful to consult a family counselor or mediator if communicating with your brother is particularly difficult, or if doing so opens old family wounds. A counselor will help you gain perspective on your situation, and can offer practical advice for how to fairly divide caregiving tasks.
Addressing the situation has the potential to open up new avenues of communication and understanding, and bring your family closer. Even if the response from your brother is disappointing, you'll feel better for dealing with the situation, rather than suffering in silence and allowing your resentment to build.