Hi, the weaving problem first, check the front wheel bearings, headstock bearings and check the wheels true, it might even be a degraded damaged or unevenly worn tyre. ive got an 01 too and the spluttering / coughing you describe sounds similar to mine, ive just fitted a T R E and its slightly better, i\´m thinking its probably going to need a power commander to sort it out fully although ive not checked everything myself as the dealer i bought it off reckoned they had fully serviced it, hope this helps 
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