Also keep in mind, for us he's experiencing it over the last century, but he could've popped up to some other star system and had adventures there for 200 years without having to regenerate, and then come back, any given time he got in the TARDIS and didn't have a companion. Time travel doesn't limit his experience of time to just the point where we view him; he can age 40 years in the year 2943-2983, bounce back to 1801, see some people, go back to caveman times to be there for 100 years, and then come to 1803. Only two years passed for them, but he's 100 years older.

Or make it worse, he goes back to 1799... 100 years older :D.