Oops I didn't even realise that 4faces had correlated the 'postively' with its antonym 'negatively'. Good call."Positively" has the same meaning that "really" would in this sentence; it serves to emphasize.
This is not a use of heaving with which I'm familiar, though the meaning is more or less obvious: it is extremely full of hotels and B&Bs. They are so densely packed that, hyperbolically, the place seems to swell or pulse with them.
http://www.merriam-webster.com/dictionary/heave1: labor, struggle 2: retch 3 a: to rise and fall rhythmically b: pant
4 a: pull, push <heaving on a rope> b: to move a ship in a specified direction or manner
5: to rise or become thrown or raised up