RE: 16 month old not interested in walking
Well, disclaimer is that obviously without seeing him and evaluating him, I can't really say specifically ;)
In general though, the normal range for walking is anywhere from 9-10 months up to 18 months. 18 months is the later end of normal, but still technically in the "normal" range, and he's not even there yet ;) The average is about 13 months, but there's a big range of normal for walking. My son walked at 13.5 months and I'm a PT ;) Not late at all. 16 months really isn't very old.
One of the biggest things to look at in general IMO is to see if the child has the precursory skills. Are they cruising? Pulling to stand? Walking with hands held or holding a push toy? If so, I tend to be less concerned, particularly if they haven't hit the 18 month mark.
It sounds like he's doing a lot of the right precursory stuff. Standing on his own, cruising, walking with hands held, climbing...all really positive signs.
You can try lowering the level of support you provide when he's walking w/ hands held. If you are holding them at (his) shoulder height, you could try lowering them to chest/nipple height. Once he can walk with hands held at that height, try lowering his hands toward his tummy a bit more. Progressively lower the level at which you give him support, but give him enough that he's still *willing* to walk. If you push too hard/too fast, he may just decide it isn't fun and stop altogether ;)
You could also look for a pushtoy...something w/ some resistance like the Radio Flyer walker wagon and see if he'll use that.
I wouldn't worry too much based on what you describe, but of course, without seeing him I can't say for sure. You can always double check w/ your physician. If he's not walking by 18 months I'd be more inclined to call early intervention at that point, but it sounds like he's on the right track ;)
HTH
Mama to DS-2004
DD-2006
and a new addition-ds born march 2010