While it may well be worth keeping the old Schwinn - it will never be a competitive tri bike.....

New steel bikes aren't necessarily heavy, but old ones from the 70's generally are. Parts will be hard to come by and many/most new modern parts will be incompatible with this old bicycle.

Keep the Schwinn - use it for running around, every day riding, fix it up as a project bike, but if you want to get serious about your tri's look for a newer road bike or a tri bike.