If both 340 spine and heavier spined arrows (maybe 300's?) are doing the same thing, sounds like a tuning issue. BH's will pick up any flaws in your setup (or form) and magnify them more than you can notice shooting field points. Maybe a stupid question, but are you sure your BH's are the same weight as the field points you were shooting? If so, I'd guess your rest or string loop needs adjustment. You didn't say anything abuot whether or not they were porposing or fishtailing during flight.
If tuned correctly, field points and BH's of the same weight, should have the same point of impact (i.e., BH's should shoot the same as field points). If not, you definitely need to do some tuning. Of course this assumes everything else is already OK too (i.e., arrow spine, adequate FOC, etc., etc.).
ET