A simple gist demonstrating how one could use Autolayout to dynamically grow a view.

ConstraintViewController.m

#import "ViewController.h"

@interface ViewController ()

@property (weak, nonatomic) IBOutlet NSLayoutConstraint *bottomConstraint;
@property (weak, nonatomic) IBOutlet UIButton *addButton;
@property (weak, nonatomic) IBOutlet UIView *containerView;
@property (nonatomic, weak) UIView *lastView;

@end

@implementation ViewController

- (void)viewDidLoad {
    [super viewDidLoad];
    // Do any additional setup after loading the view, typically from a nib.
    
    self.lastView = self.addButton;
}

- (void)didReceiveMemoryWarning {
    [super didReceiveMemoryWarning];
    // Dispose of any resources that can be recreated.
}

- (IBAction)addButtonTapped:(id)sender {
    UIView *newView = [[UIView alloc] initWithFrame:CGRectZero];
    newView.translatesAutoresizingMaskIntoConstraints = NO;
    newView.backgroundColor = [UIColor redColor];
    [newView addConstraint:[NSLayoutConstraint constraintWithItem:newView
                                                       attribute:NSLayoutAttributeHeight
                                                       relatedBy:NSLayoutRelationEqual
                                                          toItem:nil
                                                       attribute:NSLayoutAttributeNotAnAttribute
                                                      multiplier:1.0
                                                         constant:35]];
    
    [self.containerView addSubview:newView];
    [self.containerView addConstraints:[NSLayoutConstraint constraintsWithVisualFormat:@"V:[lastView]-(14)-[newView]"
                                                                     options:NSLayoutFormatAlignAllCenterX
                                                                     metrics:nil
                                                                        views:@{@"lastView" : self.lastView, @"newView" : newView}]];
    [self.containerView addConstraints:[NSLayoutConstraint constraintsWithVisualFormat:@"H:|-(10)-[newView]-(10)-|"
                                                                     options:NSLayoutFormatAlignmentMask
                                                                     metrics:nil
                                                                        views:@{@"newView":newView}]];
    
    [self.containerView removeConstraint:self.bottomConstraint];
    self.bottomConstraint = [NSLayoutConstraint constraintWithItem:self.containerView
                                                         attribute:NSLayoutAttributeBottom
                                                         relatedBy:NSLayoutRelationEqual
                                                            toItem:newView
                                                         attribute:NSLayoutAttributeBottom
                                                        multiplier:1.0
                                                          constant:14];
    [self.containerView addConstraint:self.bottomConstraint];
    
    self.lastView = newView;
}
@end