If your Weaver brand base is cut with weaver cross slots then the Seekins picitinny cross members won't work. Weaver rings will work on a picitinny base though but not the other way around.
"Military standard, MIL-STD-1913 "Picatinny rails" date from the early 1990s and have very strict dimension and tolerance standards. The Picatinny has rail of very similar profile to the Weaver, but the slot width is 0.206 in (5.23 mm), and by contrast with the Weaver, the spacing of slot centers is consistent, at 0.394 in (10.01 mm). Many rail-grabber-mounted accessories can be used on either type of rail, and generally accessories designed for a Weaver system will generally fit Picatinny rails - although not versa. The Picatinny locking slot width is 0.206 in (5.232 mm) and the spacing of slot centers is 0.394 in (10.008 mm).[2] Because of this, with devices that use only one locking slot, Weaver devices will fit on Picatinny rails, but Picatinny devices will not always fit on Weaver rails."