The president of Manhattan, Scott Stringer, waived his review period and submitted a recommendation in favor of rezoning a swath of the Upper West Side yesterday, a day after Community Board 7 unanimously approved the plan. The rezoning, which will likely be passed by the City Planning Commission and the City Council, would limit the height of new buildings in the area, as well as provide incentives for affordable housing. Developers along Broadway could build up to 145 feet, or 14 stories, if they built affordable housing units. Buildings on side streets would be subject to lower height limits. Many in the neighborhood rallied around the need to limit heights in response to two high-rise towers built by the developer Extell at Broadway and 100th Street. Many noted that the rezoning would be insufficient to preserve the character of the neighborhood, but nonetheless backed the plan. “It’s the best we could get,” the vice president of West Siders for Responsible Development, Bill Crane, said. “The longer we wait the longer developers will have to put up these gigantic high-rises.”