My first thought is a bad battery, as I haden't started the bike for about 10 days when it first "barely" started weakly. Started it two more times after only riding about a mile between each time, third time was very very weak, and almost left my stranded at a gas station. 

Got the bike back home, tried to start again the next day, and it would turn over a bit, but wouldn't start, and now it's not turning over. 

However, my question is the headlights and all instruments remain illuminated, does this sound like a weakening battery?

I want to attempt a jump start, is it safe to jump start from a car using positive battery terminal and grounding to frame with black jumper cable?

Simpl answer is YES best answer is fully charge the battery and try it on its own

rclarkbow wrote:.....
I want to attempt a jump start, is it safe to jump start from a car using positive battery terminal and grounding to frame with black jumper cable?

When jumping you really should connect the black cable directly to the negative terminal on the battery.

The battery sounds like it's dead. If it's a lead acid type, check the levels in each cell. The plates should be covered.
It's possible you aren't getting a proper charging voltage from the alternator.
The best thing to do first is to use a DMM to measure the voltage of the battery at rest (static voltage). Should be around 13.0V  Below 12.45V and your battery is kaput.
If you can get the engine running, then measure the voltage at 2,000rpm (charge voltage). Should be around 14.0V

Take the battery out of the bike.  Put it on a charger(not a maintainer/trickle charger) overnight and then take it to an auto parts store to have it load tested.  That is the only way to really tell if the battery is any good. 

How old is the battery?  A lot of batteries are only good for 3 or 4 years.  Being a northern bike, winter storage can be pretty hard on a battery, especially if the bike was put into storage with anything less than a full charge.

Once the bike is running again, do the check on the alternator.  As mentioned, at 2000 rpm there should be at least  13.8 to 14.0 volts at the battery terminals.  Speaking of terminals, they should be shiny clean and tight.  Good connections are important not only to get all the current necessary to the starter, but loose terminals will also prevent the battery from taking a full charge. 

A weak alternator output is often the result of worn brushes.  If they need to be replaced, it's a good idea to get a complete voltage regulator assembly with brushes to replace all the wear items at the same time.  Around here, I can get the alternator "rebuilt" with new brushes and bearings for about $120.

As to your question about lights.  A weak battery can run the lights since they only draw about 10 amps where the starter can draw as much as 75 amps.   Good lights but weak starter action is usually a good sign that the battery has a lot of internal resistance caused by deterioration of the plates.

Don't be tempted to confuse Voltage with cranking amps. I have had several batteries (in various machines) where the voltage after a charge looked OK but they just didn't have the Oooomph (technical term for cranking amps ) anymore

Also need to confirm your charge light comes on and then goes off.